Novak Djokovic welcomed the ongoing 'GOAT' discussion alongside Rafael Nadal and Roger Federer after the world number one took another step towards an historic grand slam title at the US Open.

Djokovic, Nadal and Federer share the most men's slams in history with 20 but the former has the chance to break the record at Flushing Meadows, where the top seed dismantled unheralded Dutchman Tallon Griekspoor 6-2 6-3 6-2 in the second round on Thursday.

Serb star Djokovic is also bidding to become just the third man to complete a calendar Grand Slam and the first to sweep all four majors in a year since Rod Laver in 1969.

It is widely debated who is the greatest player of all time among Djokovic, Nadal and Federer – the latter two are both absent from this year's US Open due to injury.

After reaching the third round in New York, Djokovic was asked who the better player on a neutral surface is, given Nadal's clay-court dominance and Federer's grass-court expertise.

"It's difficult to say who is better. Three of us, we're all so different. We have different styles," Djokovic said during his post-match news conference.

"We have different trajectories or journeys to where we are at this moment. We all had tremendous success, some more particularly on one surface, some the other surface.

"We do complement each other. I think the rivalry between the big three, so to say, it's phenomenal for our sport.

"So the more traction, the more conversation there is around the three of us, the GOAT discussion, et cetera, the better in general for our sport. I hope people still keep on talking about it."

Djokovic added: "I think actually one of the best I think images that I've ever seen from tennis is them [Nadal and Federer] playing on a half-grass, half-clay court.

"I thought that was fantastic. Whoever came up with the idea was genius. As a tennis fan, I enjoyed that very much."

Djokovic hit 33 winners, fired down 13 aces and broke six times throughout a dominant performance against Griekspoor under the Arthur Ashe Stadium lights.

The 34-year-old also improved to 53-1 against non-top 100 opponents at majors, while he is now 13-0 against them at the US Open.

Kei Nishikori awaits Djokovic, who owns a 17-2 head-to-head record against the 2014 US Open runner-up.

"We played many times. I have very good score against him," Djokovic said of Nishikori. "I lost I think last time here in New York in semis in 2014. Historically I think his most successful grand slam is here. He's one of the quickest and most-talented players that I've seen in my lifetime, in my career.

"I think it's important for me to serve well and try to take off the pace a little bit because he likes the pace. He likes to hit the ball early, protect the line. But I know his game well. We played in Olympic Games. I know what's expecting me. I look forward to a good challenge."

History-chasing world number one Novak Djokovic cruised through to the third round of the US Open at the expense of Tallon Griekspoor 6-2 6-3 6-2.

Djokovic is bidding to become just the third man to complete a calendar Grand Slam and the first to sweep all four majors in a year since Rod Laver in 1969.

The top seed, who is also pursuing a record-breaking 21st slam crown – currently level with injured stars Rafael Nadal and Roger Federer on 20 – outclassed Griekspoor in one hour, 39 minutes on Thursday.

Awaiting Djokovic is 2014 US Open finalist and Japanese star Kei Nishikori in the third round.

Djokovic, who withstood a spirited challenge from Holger Rune in the opening round before the teenager succumbed to cramps, asserted his dominance against Griekspoor from the outset on Arthur Ashe Stadium.

Boasting a 14-0 record in second-round matches at the US Open, Djokovic only lost one point on his first serve in the opening set and fired down five aces, while hitting 13 winners and converting two of his three break points.

While world number 121 Griekspoor managed to break Djokovic's serve in the second set, the Serb was typically efficient as he builds towards another shot at history in New York.

Coming to the net more in the third set, Djokovic was determined to get off the court as quickly as possible and he did just that – saving three break points en route to another third-round appearance at the year's final slam.

Data slam: Djokovic continues strong record

The 34-year-old came into the contest with a 52-1 slam record against non-top 100 opponents. Djokovic improved to 53-1 – his lone loss to world number 117 Denis Istomin at the 2017 Australian Open – and a perfect 13-0 at the US Open with his straight-sets victory.

WINNERS/UNFORCED ERRORS

Djokovic – 33/20
Griekspoor – 20/28

ACES/DOUBLE FAULTS

Djokovic – 13/5 
Griekspoor – 5/2

BREAK POINTS WON

Djokovic – 6/10
Griekspoor – 1/4

World number one Ash Barty said her serving struggles are "not a concern" after advancing to the US Open third round.

Barty continued her quest for a third grand slam title and first US Open crown with a 6-1 7-5 win over teenage prodigy Clara Tauson on Thursday.

Reigning Wimbledon champion Barty hit 33 winners and fired down 11 aces to see off the 18-year-old on Arthur Ashe Stadium in New York.

Barty, though, had to stave off a late challenge just like the top seed did against Vera Zvonareva in the opening round.

After she faltered to serve out the match at 5-4 in the second set of her victory over Tauson, Barty said: "It's happened a few times, but I have won 40-odd matches [this year] and it hasn’t happened a lot.

"It's just a few of those games I haven't been able to get up and hit my spots on first serves.

"When you give good players looks at second serves, you're going to get hurt. It's simple as that. It’s not a concern."

Barty leads the WTA Tour this season for titles won (five), match victories (42), finals reached (six), aces (319) and top-10 wins (seven).

"There's room for improvement, without a doubt, but there's room for improvement every single day," said Barty, who has never reached the quarter-finals at Flushing Meadows.

"Credit to her, she was a little bit more aggressive in that second set. I got a little bit passive and just let my energy drop and allowed her back in.

"We'll go back and have a chat about the matches and, once we get back on the practice court, try and fix a few things up, trust myself and trying to continue to play how I want to play."

Next up for Australian star Barty is either 2020 US Open quarter-finalist Shelby Rogers or Sorana Cirstea.

Alexander Zverev believes his comeback victory over Novak Djokovic at the Olympics has paved the way for his fine start at the US Open.

Zverev came from a set down to defeat world number one Djokovic 1-6 6-3 6-1 at the semi-final stage in Tokyo, with the German going on to claim gold by beating Karen Khachanov in straight sets.

The world number four carried the winning form to Cincinnati, triumphing at the Western and Southern Open, and has made a smooth start at Flushing Meadows, where he lost out to Dominic Thiem in last year's final.

Zverev did not offer up a single break point in a dominant first-round win over Sam Querrey, and lost only four games when cruising past Albert Ramos-Vinolas 6-1 6-0 6-3 on Thursday.

"The process started at the Olympics for me, and the match against Novak," Zverev told reporters.

"That kind of started it off, because I was down badly, and I managed to win with great tennis.

"It was very important for me to kind of back it up in Cincinnati, because a lot of the times players that for the first time in their career win something really big like a grand slam title or a gold medal, they do tend to go downhill a little bit.

"So it was important for me to go to Cincinnati, to a place where I have never won a match before this year, and have a great tournament."

Another motivation for Zverev is the cruel fashion in which he lost to Thiem last year, when he surrendered a two-set lead.

"I mean I was the first man in 785 years to lose a US Open from two sets to love up and being a break up in the third set, serving for it in the fifth set, being two points away multiple times, it was painful," Zverev said with a smile.

"I still remember it, I remember it every single time I walk on this board but I take it as motivation because I'm back here to hopefully play a great tournament and win a grand slam title, that's what I’m here to do."

Zverev has now tallied up 40 wins in 2021 and 13 on the bounce, though the 24-year-old - who could meet Djokovic in the semi-finals - knows he has to maintain his strong service game to keep his best tennis.

"My serve is kind of the key to my game. When it's working I'm playing great. When it's not, I'm losing matches like I did at Wimbledon," he said.

"It's no secret that my serve is probably the most important shot in my game, and I'm happy with how it's working. The matches are not going to get easier and I will need that to be my weapon.

"I think it was always a problem of mine at the beginning of my career that I always spent a lot of hours, a lot of time in the beginning of grand slam tournaments. So it's nice to have two matches, winning [them] in straight sets."

The US Open was mounting a clean-up and safety check operation on Thursday after being affected by a deadly storm that struck New York City. 

There would be no play before 12:00 local time (16:00 GMT), an hour later than matches usually get under way, and spectators were told they would not be allowed into the grounds until 11:00 at the earliest. 

Severe weather hit New York and New Jersey on Wednesday, with the tail-end of Hurricane Ida striking the area and causing at least nine deaths. 

Eight of those deaths recorded in New York resulted from basements flooding, the New York Post reported, with the flash flooding causing chaos in large parts of the city. At one point, 3.15 inches of rain fell in an hour, a record for the Big Apple. 

Tournament organisers were carrying out inspections to determine whether safety of visitors to the Flushing Meadows grounds could be assured. 

The US Open said in a statement: "We appreciate your patience as we evaluate the readiness of our site. The safety of our fans, players and staff is of the utmost importance. 

"We will be issuing an update to the schedule including gate opening and match start times. The current plan will not open gates before 11:00 am." 

The storms were so unusually powerful on Wednesday that the late-night match between Kevin Anderson and Diego Schwartzman on the covered Louis Armstrong Stadium was affected by rain, with water gusting in through openings despite the protection. 

It was moved to Arthur Ashe Stadium to be completed, with its original court left drenched. 

Transport in New York early on Thursday was proving problematic, with the Metropolitan Transportation Authority, responsible for the local bus and subway system, announcing an "extremely limited" service and urging customers to "stay home if you can". 

Ash Barty and Novak Djokovic, along with Olympic champions Alexander Zverev and Belinda Bencic, are among those due in action on Thursday. 

Men's tennis would be a safe environment for any gay player ready to announce their sexuality, three of the brightest young talents in the game have said.

Speaking on the US Open's first Pride Day, Stefanos Tsitsipas, Daniil Medvedev and Felix Auger-Aliassime said players should not fear coming out.

A number of the best-known women's players of all time have been lesbian, including Martina Navratilova, Billie Jean King and Amelie Mauresmo.

However, there have been few modern-era 'out' gay stars on the men's ATP Tour, with Navratilova having said in the past that those that exist have been "so far in the closet I don't know who they are".

Russian world number two Medvedev said: "From my side, I think everybody would be super open if somebody would come out on the ATP Tour.

"The other question is: are there any gays on the ATP Tour? Again, until somebody comes out, you cannot know unless you're his best friend and you know what he goes through.

"I think it's great from the US Open, this initiative. I think the ATP honestly is doing a good job, also especially internally trying to provide info and to just make sure that if anybody wants to come out, he's gonna feel safe and secure.

"All the players would be happy for the guy if he does it."

Canadian rising star Auger-Aliassime, who like Medvedev and Tsitsipas has reached round three at Flushing Meadows, explained it was important for the tour to let players be themselves.

On the women's tour, Belgian players Alison van Uytvanck and Greet Minnen are engaged, while there are a number of other players from the LGBTQ (lesbian, gay, bisexual, transgender, queer/questioning) community.

But the men's tour in recent years has seen no such prominently out players, which world number 15 Auger-Aliassime finds surprising, given the high number of professionals.

"Recently I've started doing a survey inside the ATP about the LGBTQ+ community," Auger-Aliassime said.

"It's important these days to be aware of that and to be open-minded and the ATP needs to do that, in today's time it's needed.

"The reason we don't have openly gay players on the ATP Tour, I'm not sure of the reason, but I feel me, as a player, it would be very open, very welcome. Statistically there should be some, but for now there's not."

Tsitsipas was asked whether the tour would be a "safe space" now, for any player considering coming out.

"I think so. They would be supported, for sure," said the Greek world number three, speaking on Wednesday's Pride Day in New York.

"I don't know how it is in other sports. I see no reason, for example, a tour like the ATP not to accept something like this."

Sloane Stephens sent Coco Gauff spinning out of the US Open – then joined the clamour to stop toilet break "gamesmanship" in tennis.

In Wednesday's opening night match on Arthur Ashe Stadium, former champion Stephens took the fast route past world number 23 Gauff, speeding to a 6-4 6-2 victory.

Now ranked 66th, Stephens won at Flushing Meadows in 2017 and was tipped by Gauff to challenge for the title again this year. By beating Madison Keys and now Gauff, Stephens is showing she still has major game, and another former champion in Angelique Kerber could be her third-round opponent.

Gauff, now 17, has known Stephens for over seven years, having attended the now 28-year-old's 21st birthday party.

But the American pair put friendship to one side for their showdown, with Gauff, who had been fancied by many to go deep this fortnight, having her threat stifled by an in-form Stephens.

"I think the last time we hit, she was probably like 12. It was a little bit different," Stephens said afterwards.

"It's just been really nice to see her game kind of evolve and the things that she's doing, like how she's able to turn so much defense into offense and kind of do those movements. She is great at the net. She has a really great all-around game. It's been really nice to see.

"She's different from a lot of the up-and-coming players we're seeing now that are just super hard hitting, not much variety. She has a lot of variety. I think a lot of the younger girls, there's half that are very hard hitting and half that have a lot of variety. I think she's in the bucket with a lot of variety."

Gauff was asked whether Stephens could now be considered a title contender and replied: "Yeah, definitely. Today she was playing well. I knew these last couple of tournaments she's been playing better and better. I hope that she can make it all the way to the end.

"Obviously if you are going to lose, you want to lose to the champion. I think that I feel like I've learned that I'm capable of making it far in slams. I think if I tighten up a few things, that I'm capable of winning one."

The debate over toilet breaks in tennis was sparked by Andy Murray being furious with Stefanos Tsitsipas for spending eight minutes in the bathroom before tackling the Scot in the deciding set of their first-round match.

Murray, frustrated to be left waiting for his opponent to reappear, followed up his Monday night fury with a tweet that charged Tsitsipas with taking twice as long to visit the toilet as Amazon mogul Jeff Bezos took to travel into space.

There was no such spat in Stephens' quickfire win over Gauff, but the rules on spending a penny have been the currency of many a news conference this week.

"I honestly just thought Andy's tweet was really funny," said Stephens. "I didn't see exactly what happened. I'm not sure. I just thought it was hilarious. We all are like huge Andy fans. We love him.

"I can't speak for what happened in that match, but I do know on the girl's side, there still is a lot of that. It's gamesmanship.

"I think there definitely needs to be a rule or changes. They make a lot of rule changes for smaller things, like they took one minute off the warm-up. If someone goes to the bathroom for nine minutes, no one says anything.

"Six, eight minutes is a long time to leave a match. That changes the whole momentum of a match. If you're changing your clothes, what are you changing? What are you doing in there?

"When you get into six, seven, eight, nine minutes, okay, what are you doing in there? Do you need help? I can come help you. Like, what's happening? I think that's more where the issues are because it just becomes pure gamesmanship."

Two-time major winner Victoria Azarenka says it is "bizarre" that fans need to be vaccinated to attend the US Open but not the players.

The 2021 US Open marks the first tennis tournament where fans must show their proof of COVID-19 vaccination in order to attend matches inside the Flushing Meadows venue. The decision was made less than 72 hours prior to the first matches at the US Open.

Azarenka, who defeated Italian Jasmine Paolini 6-3 7-6 (7-1) in the second round on Wednesday, said there was a double standard applied for fans compared to players who are not required to be vaccinated to play.

"I want to start this conversation between our players, because to me that's a bit bizarre that fans have to be vaccinated and players are not," three-time US Open finalist Azarenka told reporters.

"I think it's inevitable that it will be mandated at some point, like other leagues are doing.

"I don't see the point of stalling it, because I think we all want to be safe, we all want to continue doing our jobs, and I know there is a lot of discussions about it."

She added: "I hope that as an association we make the best decision for our business, for our health, for the tournaments and for the public."

On Saturday, Briton Andy Murray voiced his opinion that players need to be vaccinated, saying it is their responsibility as they travel the world to play.

Numerous top players including Novak Djokovic, Stefano Tsitsipas and Daniil Medvedev have previously spoken about their concerns about getting vaccinated.

Medvedev would not be drawn on Azarenka's comments after he defeated Dominik Koepfer 6-4 6-1 6-2 in the second round on Wednesday.

"Tough to answer this question," Medvedev told reporters. "I think everybody can have his own opinion.

"I understand why they did it to the fans. So far it has not been applied to the players. We as players, we can just follow the guidelines and the rules. That's all we can do.

"I think it's not for players to decide, because that's why we have governing bodies in tennis."

Stefanos Tsitsipas has defended his "personal need" for long bathroom breaks after being jeered during his four-set second round win over Adrian Mannarino at the US Open on Wednesday.

The world number three triumphed 6-3 6-4 6-7 (4-7) 6-0 but was booed by the Arthur Ashe Stadium crowd after taking a bathroom break which exceeded seven minutes.

The Greek was criticized by Andy Murray, who said he lost respect for Tsitsipas after taking a lengthy break ahead of the final set in their five-set first round epic on Monday.

Alexander Zverev weighed in on the discussion, claiming Tsitsipas was communicating with his coach during his bathroom breaks, labelling them "ridiculous" and saying he had broken an "unwritten law".

Tsitsipas reverted to the rule book in his defence after beating Mannarino, insisting he had done nothing illegal and longer breaks were part of his "personal needs".

"It's just my personal needs," Tsitsipas told reporters. "Some people have other needs. Some people take much more than 25 seconds between points, which is fair.  

"I've done everything the right way. If I haven't I should be penalized. I completely agree with it. I should get a fine or be penalized if I haven’t followed whatever I've done correctly. But as far as I know, it is a necessity, it is a need when I'm out there playing and performing."

Tsitsipas said he felt fans who booed and jeered did not understand the game or his need to take longer bathroom breaks.

"I haven’t done anything wrong so I don't understand," he said. "The people love the sport, they come to watch tennis. I have nothing against them. But some people don't understand. They haven't played tennis at high level to understand how much effort and how much difficult it is to do what we are doing."

He added: "It is important. First of all, you carry less weight on you with all the sweat. You feel rejuvenated, you feel fresh, and you don't have all the sweat bothering you and coming in your face, on your fingers, everywhere all over your body. It makes you feel better.

"For me it is important to take that break. For someone else probably not. And everyone has his own time. I try and be as quick as I can. Sometimes I just need a bit more time."

Tsitsipas added that he was taken aback by the public criticism from Murray and Zverev.

"I never complain of what other players do," the 23-year-old French Open runner-up said. "My parents have taught me not to watch other people's business and concentrate on myself. Do my job.

"I just don’t understand when some players go and criticize other players, or during a match they put too much emphasis on it."

There have been calls for a hard cap on the permitted time for bathroom breaks, which American Sloane Stephens agreed with, speaking after her straight-sets win over 21st seed Coco Cauff.

"I don't think you should be gone from the court for six-eight minutes," Stephens said. "It's a long time to leave a match. That changes the whole momentum of a match.

"I can't speak for what happened in that match, but I do know on the girls' side, there still is a lot of that. It's gamesmanship.

"I think there definitely needs to be a rule or changes. They make a lot of rule changes for smaller things, like they took one minute off the warmup. If someone goes to the bathroom for nine minutes, no one says anything."

Two-time major winner Victoria Azarenka says it is "bizarre" that fans need to be vaccinated to attend the US Open but not the players.

The 2021 US Open marks the first tennis tournament where fans must show their proof of COVID-19 vaccination in order to attend matches inside the Flushing Meadows venue. The decision was made less than 72 hours prior to the first matches at the US Open.

Azarenka, who defeated Italian Jasmine Paolini 6-3 7-6 (7-1) in the second round on Wednesday, said there was a double standard applied for fans compared to players who are not required to be vaccinated to play.

"I want to start this conversation between our players, because to me that's a bit bizarre that fans have to be vaccinated and players are not," three-time US Open finalist Azarenka told reporters.

"I think it's inevitable that it will be mandated at some point, like other leagues are doing.

"I don't see the point of stalling it, because I think we all want to be safe, we all want to continue doing our jobs, and I know there is a lot of discussions about it."

She added: "I hope that as an association we make the best decision for our business, for our health, for the tournaments and for the public."

On Saturday, Briton Andy Murray voiced his opinion that players need to be vaccinated, saying it is their responsibility as they travel the world to play.

Numerous top players including Novak Djokovic, Stefano Tsitsipas and Daniil Medvedev have previously spoken about their concerns about getting vaccinated.

Medvedev would not be drawn on Azarenka's comments after he defeated Dominik Koepfer 6-4 6-1 6-2 in the second round on Wednesday.

"Tough to answer this question," Medvedev told reporters. "I think everybody can have his own opinion.

"I understand why they did it to the fans. So far it has not been applied to the players. We as players, we can just follow the guidelines and the rules. That's all we can do.

"I think it's not for players to decide, because that's why we have governing bodies in tennis."

Naomi Osaka was due to face Olga Danilovic on Wednesday, but the defending US Open champion was handed a walkover into the third round. 

Osaka, who defeated Marie Bouzkova in the first round to start her title defence at Flushing Meadows, is hunting her fifth grand slam title and third in New York. 

Serbian youngster Danilovic, who is being mentored by ATP world number one Novak Djokovic, defeated American Alycia Parks in straight sets on Monday but had to pull out of her second-round tie with Osaka due to a viral illness. 

However, the 20-year-old stressed she had not tested positive for COVID-19. 

"Hi everyone… I am so sad to have to withdrawal [sic] from my match this morning. I have been feeling unwell these past few days dealing with a non-COVID related viral illness," Danilovic wrote in an Instagram post. 

"I was really looking forward to playing against Naomi on Arthur Ashe Stadium today, but [it was] not to be this time. 

"I just want to say [a] big thank you to medical staff here [at the] US Open and [to] everyone for your support and I cannot wait to be back in New York at this amazing tournament next year." 

Osaka will face Leylah Fernandez in the third round on Friday after the Canadian beat Kaia Kanepi 7-5 7-5. 

Another of the big names, Simona Halep, also progressed, with the two-time grand slam winner seeing off Kristina Kucova 6-3 6-1. 

Novak Djokovic's quest to become only the third man to complete a calendar Grand Slam and first to win 21 majors started with a 6-1 6-7 (5-7) 6-2 6-1 victory over Holger Rune at the US Open.

Not since Rod Laver in 1969 has a man won all four majors in the same year – Djokovic arrived in New York as the Australian Open, French Open and Wimbledon champion.

Also eyeing history as the first man to claim 21 slams – currently tied with injured superstars Rafael Nadal and Roger Federer – Djokovic navigated his passage through to the second round at Flushing Meadows on Tuesday.

Danish qualifier Rune was making his grand slam main-draw debut, but the 18-year-old was not overawed under the bright Arthur Ashe lights.

However, Rune faded fast due to apparent cramps as world number one Djokovic eventually cruised through to round two of the year's final major after more than two hours.

Playing for the first time since his Golden Slam bid came unstuck at the Olympic Games in Tokyo, Djokovic looked comfortable initially, closing out a merciless opening set with an ace.

Djokovic did not face a break point, boasting 100 percent returns against first serve, barely giving Rune a break.

But that changed in the second set – the energetic Rune winding up the crowd as he raced out to a 3-0 lead before Djokovic swiftly reeled off four consecutive games to move ahead.

Rune, however, capitalised on some uncharacteristic double faults to ultimately level the match in a tie-break, much to the delight of the American crowd.

But that is as good as it got for a frustrated Rune, whose physical conditioning proved his downfall, having gone toe-to-toe with the top seed in a fearless display.

Data slam: Djokovic extends US Open streak

Back in New York for the first time since he was sensationally thrown out of the US Open last year after accidentally hitting a line judge in the throat with a tennis ball, Djokovic got the job done.

Three-time US Open champion Djokovic now remains unbeaten in opening-round matches at the tournament, with a 16-0 record.

WINNERS/UNFORCED ERRORS

Djokovic – 55/30
Rune – 24/26

ACES/DOUBLE FAULTS

Djokovic – 17/7
Rune – 1/4

BREAK POINTS WON

Djokovic – 8/14
Rune – 2/3

World number one Ash Barty was relieved but happy with her response after surviving a first-round scare against Vera Zvonareva at the US Open.

Barty – the top seed back at Flushing Meadows after skipping the 2020 event due to the coronavirus pandemic – booked her spot in the second round with a 6-1 7-6 (9-7) victory but the Wimbledon champion endured a challenging opener in New York on Tuesday.

Despite firing down 11 aces to improve her WTA Tour-leading tally to 300 in 2021, and hitting 31 winners, veteran Zvonareva was a tricky first-up opponent for Australian star Barty.

A US Open and Wimbledon runner-up in 2010, Zvonareva made life difficult for Barty in the second set, earning a chance to force a decider but the 36-year-old was unable to capitalise at 7-6 in the tie-break.

Afterwards, Barty – who ranks first this season for titles (five), match victories (41), finals reached (six) and top-10 victories (seven) – told reporters: "Obviously a tough one against Vera straight up.

"She's an experienced campaigner. She knows how to get herself into matches. I think all in all, adapting to conditions was a little bit slower than I probably would have liked [but] we're through. We have another chance to improve on that in the next round.

"I think when my back was against the wall late in that buster, I came up with some really good stuff. That's all we can ask is when your back is against the wall, you trust yourself, you go out there and pick your spots and hit them."

Two-time grand slam champion Barty – fresh off winning in Cincinnati as Clara Tauson awaits in round two – added: "It obviously got really tense in that second set - tight - and in the bigger moments I was able to be aggressive and trust myself and that was a massive thing today.

"There were a couple of games where I had lapses in concentration but I was able to come through in straight sets and now we go back to the drawing board, work on a few things and we'll be as happy as Larry.

"I'm certainly happy to be through and playing again here in New York."

Alexander Zverev has accused Stefanos Tsitsipas of behaving like a junior and disrespecting his opponents by taking such long bathroom breaks during matches.

Andy Murray was furious when Tsitsipas was off court for around eight minutes ahead of the final set in their thrilling first-round match at the US Open on Monday.

Tsitsipas also required a medical timeout for a foot problem during a pulsating contest that the world number three won 2-6 7-6 (9-7) 3-6 6-3 6-4 at Flushing Meadows.

Murray said he had lost respect for the 23-year-old, who defended his lengthy spell off court and stated he had played by the rules.

The Brit was in no mood to back down on Tuesday, however, as he tweeted: "Fact of the day. It takes Stefanos Tsitsipas twice as long to go the bathroom as it takes Jeff Bezos to fly into space. Interesting."

Zverev appeared to accuse Tsitsipas of communicating with his father and coach, Apostolos, when he took a break during their semi-final showdown at the Western and Southern Open in Cincinnati this month.

Tsitsipas responded by denying having ever used his phone during such a situation, describing the accusation as "absolutely ridiculous."

However, world number four Zverev had Tsitsipas in his sights once again after beating Sam Querrey 6-4 7-5 6-2 in New York.

The German said: "It's happening every match. It's not normal. It happened to me in the French Open, to Novak at the finals [of the] French Open. I think Hamburg against [Filip] Krajinovic he was complaining, against me in Cincinnati was ridiculous, and now here again. I think players are catching up with that.

"He's the number three player in the world. I do not believe he needs to do that, because if you're top three in the world, you're one of the best in the sport.

"These kind of things happen at junior events, at Futures, at Challengers maybe, but not when you're top three in the world.

"You're allowed to do that but it's like an unwritten rule with players. I have been breaking rackets, I go insane sometimes and all that but one thing I'm very proud of, and I'll keep for the rest of my career, is I win and I lose by playing tennis on the tennis court."

Zverev reiterated his grievance with Tsitsipas having taken such a lengthy break during their meeting in Cincinnati.

"I didn't ask that question in Cincinnati, which I was very surprised at, because I was going to answer that very truthfully and honestly," he said.

"He's gone for 10-plus minutes. His dad is texting on the phone. He comes out and all of a sudden his tactic completely changed. It's just not me but everybody saw it. The whole game plan changes.

"I'm like, either it's a very magical place he goes to or there is communication there. But I also don't want to disrespect him. He is a great player, he is number three in the world for a reason. He's winning tournaments and playing incredible tennis this year for a reason, so it's not only that.

"But I do believe, and Andy said it as well, there is some level of respect that everybody needs to have between players.

"I feel like sometimes - or he might just go to the toilet. We don't know that, that's also possible. But it just happens too often, I would say."

Andy Murray has doubled down on his criticism of Stefanos Tsitsipas by joking that his US Open conqueror's bathroom breaks take twice as long as Jeff Bezos' trips to space.

World number three Tsitsipas beat Murray 2-6 7-6 (9-7) 3-6 6-3 6-4 in a thrilling five-set battle in the opening round at Flushing Meadows on Monday.

The opening-day showdown was overshadowed by Tsitsipas' controversial bathroom break ahead of the decisive fifth set – the Greek star spending around eight minutes off court, much to the frustration of Murray.

Tsitsipas also required a medical timeout for an apparent foot problem after losing the third set to 2012 champion Murray, who was far from impressed following almost five hours of action.

Speaking after the match, Murray – who failed to progress beyond the first round of the US Open for the first time in 15 appearances – said he had lost respect for Tsitsipas and suggested his opponent had deliberately attempted to disrupt his flow. 

Tsitsipas defended his lengthy break, insisting he had played by the rules and that he would speak to Murray face-to-face should the Briton wish to take the issue further.

Rather than resolving the matter, however, Murray aimed another dig at Tsitsipas with a sarcastic message on his personal Twitter account on Tuesday, comparing the stoppage to the 10 minutes and 10 seconds it took billionaire Bezos to fly to space last month.

"Fact of the day. It takes Stefanos Tsitipas (sic) twice as long to go the bathroom as it takes Jeff Bazos (sic) to fly into space. Interesting," he posted.

With the win over Murray, Tsitsipas became the 10th active player to defeat all four members of the 'Big Four' – Murray, Novak Djokovic, Rafael Nadal and Roger Federer.

Tsitsipas will meet world number 44 Adrian Mannarino in the second round on Wednesday.