Rafael Nadal says his third-round win over Richard Gasquet was his best of this year's US Open as he works his way back after the abdominal tear that ended his Wimbledon campaign.

Prior to the US Open, Nadal had only played once since withdrawing from the Wimbledon semi-final against Nick Kyrgios in early July, losing to Borna Coric in Cincinnati.

The second seed got past Rinky Hijikata and Fabio Fognini in four sets in the first two rounds at Flushing Meadows before Saturday's 6-0 6-1 7-5 win over French veteran Richard Gasquet in two hours and 17 minutes.

"My best match in the tournament," Nadal told reporters. "Easy to say that because the other day was tough.

"But important improvement. But I need to keep going. It's a good victory for me. Straight sets for the first time. Third set had been a challenge. He increased the level.

"I went through some difficult moments. That's something that is good that I went through that and saved that moments with a positive feelings. Happy to be in the fourth round, without a doubt."

The victory over Gasquet meant he has progressed to the second week at Flushing Meadows for the 12th time in his career, although he conceded he would need to lift his level to take out the title, starting with Monday's fourth-round match with 22nd seed Frances Tiafoe.

Nadal is gunning for his third major title this calendar year in New York, having triumphed at the Australian Open and French Open.

The 36-year-old's Australian Open success in February came after minimal preparation due to a foot injury, similar to his US Open lead-up due to the abdominal issue.

"I think I played better in Australia than here going to the second week," Nadal said. "But I have zero background in terms of victories and all this stuff.

"Here I played little bit worse than in Australia, without a doubt. But the story of the year and the results on the slams have been incredible, so that helps.

"I don't know the balance, what's better or worse. But all these victories help to be a little bit more confident. It's a moment to increase, to making a step forward."

"Second week against a great player like Frances, I need to be ready to play and to raise my level. I hope to be able to make that happen.

"I know is the right moment to make an improvement if I want to keep having chances to keep going on the tournament."

Second seed Rafael Nadal continued his staggering head-to-head domination of Richard Gasquet as he cruised into the fourth round at the US Open with a straight-sets victory on Saturday.

The 22-time major winner was irrepressible across the first two sets before Gasquet rallied in the third, but Nadal triumphed 6-0 6-1 7-5 in two hours and 17 minutes.

The victory means the 2022 Australian Open and French Open champion will face 22nd seed Frances Tiafoe in the fourth round and improves his head-to-head record against Gasquet to 18-0.

Nadal, who had been shaky early against Fabio Fognini last round, was ruthless when it mattered, hitting 35 winners for the match and winning 78 per cent on his first serve.

After dropping the opening sets in his previous two matches against Fognini and Rinky Hijikata, Nadal responded with a flawless first frame that included converting three of six break points.

Gasquet's belief seemed completely gone in the second set, managing no winners, with Nadal in control. The Frenchman ended Nadal's nine-game winning run to loud applause, raising his arms in celebration and probable relief.

Nadal broke early in the third but Gasquet responded to break back, pushing hard in the third set. But the Spaniard's quality shone highlighted by his finesse with a lob helping him claim the decisive break in the 11th game.

Data Slam: Rafa's longevity on show

Saturday's win was Nadal's 30th at night at Arthur Ashe Stadium and took his tally to 22-0 at majors this year, having only withdrawn from Wimbledon due to an abdominal injury. The triumph also saw him progress to the second week at Flushing Meadows for the 12th time in his decorated career, that includes four US Open titles. 

WINNERS/UNFORCED ERRORS

Nadal – 35/23
Gasquet – 19/29

ACES/DOUBLE FAULTS

Nadal – 2/8
Gasquet – 1/7

BREAK POINTS WON

Nadal – 7/15
Gasquet – 1/7

Dominic Thiem started his bid for a second Austrian Open title with a comfortable triumph over Alexander Shevchenko.

Thiem, a 2019 winner at the tournament in his home country, prevailed 6-4 6-2 in Kitzbuhel.

He will next face compatriot Sebastian Ofner as he seeks a first title since his grand slam breakthrough at the US Open in 2020.

Ofner came from a set down to beat former world number seven Richard Gasquet 1-6 7-5 7-5.

Meanwhile, seventh seed Pedro Martinez saved six out of six break points en route to a 7-6 6-3 victory over Chilean Nicolas Jarry.

At the Croatia Open in Umag, Bernabe Zapata Miralles set up a round of 16 meeting with third seed Holger Rune by beating Croatian Dino Prizmic, who retired when facing a 6-4 3-0 deficit.

Alex Molcan is safely through to the next round after defeating Duje Ajdukovic, while French 23-year-old Corentin Moutet cruised to a straight-sets victory over sixth seed Daniel Altmaier.

Former world number 17 Cristian Garin was beaten 6-4 7-5 by Federico Coria in the first round of the Austrian Open in Kitzbuhel, while Matteo Berrettini and defending champion Casper Ruud withdrew from the tournament.

2017 runner-up Joao Sousa cruised past Vit Kopriva 6-1 7-5 and Jurij Rodionov set up a Round of 16 meeting with third seed Roberto Bautista Agut with a straight-sets victory over Hernan Casanova.

Dominic Thiem, who won the 2019 edition of the competition, will face Alexander Shevchenko tomorrow while Richard Gasquet will take on Sebastian Ofner.

2016 Croatia Open winner Fabio Fognini will not be regaining his title in Umag this year, after the seventh seed was knocked out by Colombian Daniel Galan in a 3-6 7-5 3-6 defeat.

Galan will play Giulio Zeppieri in the next round, who came from one set down to overcome world number 90 Pedro Cachin 3-6 6-1 6-4.

Fifth seed Alex Molcan plays his first game tomorrow against Duje Adjukovic, and sixth seed Daniel Altmaier will take on French 23-year-old Corentin Moutet.

Carlos Alcaraz was made to come from a set down but finally overcame Nicola Kuhn in the first round of the Hamburg European Open.

The highly rated Spanish teenager eventually downed the German wildcard 3-6 6-1 7-6 (7-3).

Kuhn, ranked 259 in the world, was aggressive early on against Alcaraz, and was rewarded with the first set.

But the 19-year-old – playing as top seed in an ATP Tour event for the first time – rallied to ease through the second set, before being made to work much harder to clinch the win on a tie-break.

Alcaraz will now play Filip Krajinovic in the second round after the Serbian also won in a third-set tie-break against Sebastian Baez 6-1 4-6 7-6 (8-6).

Three seeded players crashed out on Tuesday in straight sets, with third favourite Diego Schwartzman losing against Emil Ruusuvuori 7-5 6-4, sixth seed Nikoloz Basilashvili beaten by Aslan Karatsev 6-4 6-0, and eighth seed Holger Rune going down 7-6 (10-8) 7-5 to Tallon Griekspoor. 

Fourth seed Pablo Carreno Busta eased through against Luca Nardi 6-2 6-1, while there were also wins for Fabio Fognini, who sealed his 400th career victory, as well as Daniel Elahi Galan, Borna Coric and Francisco Cerundolo.

At the Swiss Open in Gstaad, sixth seed Cristian Garin lost 6-3 6-4 to Yannick Hanfmann and seventh favourite Hugo Gaston fell to Dominic Thiem despite winning the first set, losing 1-6 6-1 7-6 (9-7).

Elsewhere, Frenchman Richard Gasquet beat Roberto Carballes Baena 7-5 6-4, while his compatriot Benoit Paire retired hurt when a set and a break down against Elias Ymer.

A tight game between Swiss pair Dominic Stricker and Marc-Andrea Huesler saw the former prevail 6-7 (2-7) 7-6 (7-2) 6-4, and an all-Spanish affair was similarly close as Jaume Munar defeated Bernabe Zapata Miralles 6-3 3-6 7-5.

There were also wins for qualifiers Juan Pablo Varillas and Nicolas Jarry against Lorenzo Sonego and Thiago Monteiro respectively.

Casper Ruud is one match away from successfully retaining his Geneva Open title, while Cameron Norrie has a shot at redemption in Lyon. 

World number nine Ruud was a 7-6 (7-2) 7-5 winner against Reilly Opelka on Friday, putting him on the brink of a second ATP Tour crown of the season and a sixth in his past seven ATP 250 events on clay. 

The Norwegian made the semi-finals at the Internazionali d'Italia last week and maintained his momentum ahead of the French Open. 

He converted the match's only breakpoint in the penultimate game and sealed the deal in the next, dropping just five of 46 points behind his first serve throughout.

Ruud will take on Joao Sousa – who was the runner-up to Thomaz Bellucci in Geneva seven years ago – in the final after the Portuguese defeated Richard Gasquet 6-2 6-2. 

Norrie will also be hopeful of making up for a past final defeat after winning his last-four encounter with Holger Rune at the Lyon Open. 

The Briton was a set and a break up before Rune recovered to force a decider, which Norrie took for a 6-2 5-7 6-4 triumph in a little over two hours.

Norrie was beaten by Stefanos Tsitsipas in last year's final but it is Alex Molcan who stands between him and the trophy this time around. 

Molcan, who is yet to win a Tour-level title, claimed an impressive victory 7-6 (7-2) 6-2 win over Alex de Minaur. 

Casper Rudd set up a semi-final clash with Reilly Opelka by claiming a straight-sets win over Thanasi Kokkinakis at the Geneva Open, while Cameron Norrie made his third semi-final of 2022 at the Lyon Open.

World number eight Rudd, who claimed the title in Geneva last year with a straight-sets final win over Denis Shapovalov, overcame Kokkinakis 6-4 7-6 (7-3) on Thursday and will now face Opelka.

The American bounced back from losing the second set against Dutchman Tallon Griekspoor to claim a 6-4 3-6 6-3 win as he bids for his third title of 2022, and second seed Ruud said he was excited to pit himself against Opelka after securing his spot in the semi-finals.

"I expect it to be tough," Ruud said. "But I will do my best and see how I can do. I always enjoy playing against Reilly. He is a similar age to myself, and it will be another battle against him – hopefully it will be a good one."

Elsewhere, three-time grand slam semi-finalist Richard Gasquet followed up his shock win over Daniil Medvedev with a 6-2 6-4 victory over Kamil Majchrzak, and will face Joao Sousa for a place in the final after the Portuguese beat Ilya Ivashka 7-5 7-5.

At the Lyon Open, top seed Norrie battled to a 6-4 4-6 7-5 win over Sebastian Baez, spurning three match points before finally downing the Argentinian after a marathon two hours and 40 minutes clash.

The world number 11 will face Holger Rune in his semi-final contest after the 19-year-old came from a set down to beat Manuel Guinard 3-6 6-3 6-4.

The other semi-final in France will see fourth seed Alex de Minaur take on Alex Molcan after the Australian's quarter-final opponent Yosuke Watanuki withdrew after losing the first set 6-4, citing a back issue.

Molcan, meanwhile, downed Federico Coria 6-3 6-2 to reach the final four.

Daniil Medvedev was defeated on his ATP Tour return at the Geneva Open by a sparkling Richard Gasquet, a blow to the Russian ahead of the French Open

World number two Medvedev was making his first appearance since March after undergoing a hernia operation and fell to a 6-2 7-6 (7-5) defeat.

The Russian's rustiness was clear in the last-16 tussle as he racked up seven double faults and struggled to make inroads on Gasquet's second serve, with the Frenchman winning 61 per cent of points behind it.

It was the first time Gasquet overcame an opponent ranked in the top two since beating Roger Federer at the 2005 Monte Carlo Masters.

Next up for Gasquet will be Kamil Majchrzak, who beat Marco Cecchinato 6-2 6-3.

At the last-32 stage, Fabio Fognini went down 6-4 6-3 to Thanasi Kokkinakis and Albert Ramos-Vinolas succumbed to a 7-6 (7-5) 6-4 loss against Christopher O'Connell.

Johan Nikles, Nikoloz Basilashvili and Joao Sousa also advanced to the second round.

Top seed Cameron Norrie cruised into the quarter-finals of the Lyon Open by beating Francisco Cerundolo 6-4 6-4.

The Briton will face another Argentinian next in the form of Sebastian Baez, who came from a set down to beat Oscar Otte 5-7 6-4 6-2. 

Alex De Minaur also had to rally for a 1-6 6-3 6-2 win against Ugo Humbert, with Yosuke Watanuki awaiting in the last eight after the world number 263 beat Soonwoo Kwon 6-3 6-4.

Top seed Felix Auger-Aliassime fell to Sebastian Korda in the Estoril Open quarter-finals, while Casper Ruud was sent packing at the BMW Open. 

Auger-Aliassime won just 50 per cent of points behind his first serve as Korda claimed an impressive 6-2 6-2 success over the Canadian in one hour and 29 minutes. 

In the semi-finals Korda will take on fellow American Frances Tiafoe, who edged out Alejandro Davidovich Fokina 7-6 (7-5) 5-7 7-5 in a tight encounter. 

The other last-four clash will see Albert Ramos Vinolas take on Sebastian Baez. 

Ramos Vinolas bested Fernando Verdasco 6-2 6-2 to set up his meeting with Baez after the Argentine rallied from a set down to defeat Richard Gasquet 3-6 6-1 6-4. 

At the BMW Open, second seed Ruud fell to Botic van de Zandschulp in the quarter-finals. 

The Dutchman won their only previous encounter en route to the last eight at last year's US Open and he triumphed 7-5 6-1 in Munich. 

"Maybe the score is easier than it really was," said Van de Zandschulp. "The first set [was] really tight, I think. A great battle in the first one. I had some opportunities to break him in the beginning and didn't take them. Gladly [at] five-all I made the break and held the serve at 6-5. 

"[The] second set was a little bit easier, but I think I played really well today." 

Next up for Van de Zandschulp is Miomir Kecmanovic, who defeated Nikoloz Basilashvili 7-6 (7-5) 6-2. Holger Rune will continue his impressive run against Oscar Otte in the other semi-final after they overcame Emil Ruusuvuori and Alejandro Tabilo respectively. 

Andy Murray suffered one of the heaviest losses of his career in the second round of the Qatar Open, while Andrey Rublev escaped an early exit at the Open 13. 

Former world number one Murray went down 6-0 6-1 to last year's runner-up Roberto Bautista Agut in Doha on Wednesday. 

It was just the fourth occasion in which the three-time major champion has lost a match while winning only one game or fewer in his career – the last time being a defeat by the same scoreline to Roger Federer at the ATP Finals in 2014. 

Murray's fellow Briton Dan Evans also endured a second-round loss, going down 4-6 7-5 6-4 to Alejandro Davidovich Fokina – Bautista Agut's next opponent. 

Denis Shapovalov bounced back from his first-round loss to Jiri Lehecka in Rotterdam last week by dropping just eight points on serve as he claimed a 6-4 6-0 victory over Alex Molcan inside 52 minutes. 

Next up for the Canadian will be Arthur Rinderknech after the Frenchman came from a set down to defeat seventh seed Alexander Bublik 6-7 (5-7) 6-1 6-4. 

Nikoloz Basilashvili faced little trouble in overcoming Elias Ymer 6-4 7-5 and his reward is a quarter-final against Marton Fucsovics, who got the better of Kwon Soon-woo. 

Karen Khachanov and Marin Cilic will meet in the last eight after they respectively eliminated Emil Ruusuvuori and Botic van de Zandschulp. 

In Marseille, second seed Rublev was made to work hard for a place in the Open 13 quarter-finals by home hope Richard Gasquet. 

Gasquet went a break up in the third set and, after surrendering his advantage, stopped Rublev serving out the match to force a tie-break. 

However, the world number seven did not waste his next opportunity as he sealed a 4-6 6-4 7-6 (7-3) success. 

Aslan Karatsev also booked his place in the last eight, while there were wins for Frenchmen Benjamin Bonzi and Lucas Pouille too. 

Top seed Alexander Zverev returned to winning ways after a surprise fourth-round Australian Open exit when he won his first match at the Open Sud de France on Thursday.

The German world number three was bounced out at Melbourne Park by Denis Shapovalov in straight sets, but he navigated his way safely past Mackenzie McDonald to reach the quarter-finals in Montpellier.

A largely dominant Zverev won 6-2 7-6 (7-5) to set up a clash with Adrian Mannarino in the last eight, and the 24-year-old highlighted how important he felt it was to quickly get back in the swing of things after disappointment in Melbourne.

"I'm going to give myself the best chance to do well in this tournament. But obviously, I'm happy to be back here," he said of the tournament he won in 2017.

"This is a place I really enjoy coming back [to]. After the Australian Open that I had, I wanted to play tournaments before my scheduled tournaments in Acapulco, Indian Wells and Miami. I said Montpellier is the perfect fit for that, and I'm happy to be here."

The same cannot be said for Gael Monfils, who suffered a crushing 6-1 6-2 defeat to Mikael Ymer on home soil.

The Swede was practically flawless throughout, winning a whopping 83 per cent of points on first serve and 89 per cent on second, with Monfils never even sniffing out a single opportunity to break back.

Richard Gasquet is a force to be reckoned with in Montpellier and reached another quarter-final, seeing off South Korean's Kwon Soon-woo 7-5 6-4.

Frenchman Gasquet reached six consecutive finals in Montpellier while in his prime years, being crowned champion in 2013, 2015 and 2016, and finishing runner-up in 2014, 2017 and 2018. Now 35, his last quarter-final appearance in an ATP main tour event came in August at Winston-Salem.

Gasquet's fellow Frenchman Mannarino sank the hopes of defending champion David Goffin, scoring a sparkling 6-4 6-2 victory.

Fourth seed Nikoloz Basilashvili, who lost twice to Andy Murray in Australia last month, this time fell to world number 152 Damir Dzumhur of Bosnia-Herzegovina, sliding to a 6-1 5-7 6-2 defeat. Basilashvili, the world number 21, now has a record of played five, lost five, for the 2022 season.

At the Tata Open Maharashtra in Pune, there was a surprise defeat for Russian top seed Aslan Karatsev. Karatsev won a title in Sydney last month before losing to Mannarino in the third round of the Australian Open, and in his first match since that disappointment he slumped 6-2 7-6 (7-3) to Swedish qualifier Elias Ymer.

Three seeds joined Ymer in the quarter-finals, with Jiri Vesely, Emil Ruusuvuori and Stefano Travaglia all making smooth progress without dropping a set. Vesely faces Ruusuvuori on Friday, while Travaglia awaits Ymer.

Arthur Rinderknech continued his fantastic season by defeating Federico Delbonis at the European Open, while Marin Cilic battled through in the Kremlin Cup.

Rinderknech, who sits 65th in the world rankings, had not recorded a Tour-level victory before 2021 but has now triumphed 15 times after cruising past Delbonis 6-4 6-4.

The Frenchman will meet eighth seed Dusan Lajovic in the second round in Antwerp, after the Serbian downed Richard Gasquet 7-6 (7-3) 6-1 on Monday.

The other first-round clash in Belgium saw Alexei Popyrin capitulate in the third set as he succumbed to a 4-6 6-3 0-6 defeat against world number 62 Botic van de Zandschulp.

Americans Jenson Brooksby and Brandon Nakashima also booked their places in the main draw. Brooksby defeated Norbert Gombos 6-4 6-2, while Nakashima overcame Pierre-Hugues Herbert 6-2 6-4.

Meanwhile in Russia, Cilic – who has claimed the crown in Moscow twice previously – recovered from a first-set scare in his round-of-32 tie with qualifier Damir Dzumhur, eventually triumphing 6-7 (4-7) 6-1 6-1.

John Millman experienced similar difficulties, with Benjamin Bonzi claiming the first set before the Australian succeeded 6-7 (5-7) 6-4 6-3 to set up a potential second-round match against fifth seed Alexander Bublik.

Pablo Carreno Busta headlined the casualties at the Winston-Salem Open, where the top seed was shocked in straight sets by Ilya Ivashka.

The 2016 champion, Carreno Busta had his sights set on the semi-finals of the ATP 250 tournament but he suffered a surprise 7-6 (7-2) 6-3 loss on Thursday.

"Of course it's a great feeling. I had a great match today. These conditions suit me," Ivashka said. "I think he had more pressure because he's the top seed so for me it was a good challenge to see what my level is and to compete with these guys, so for me it was a great match."

Carreno Busta – who trumped world number one and 20-time grand slam champion Novak Djokovic to win bronze at the Olympic Games – was not the only seed to fall.

Richard Gasquet and Frances Tiafoe also crashed out in the quarter-finals following defeats to Emil Ruusuvuori and Mikael Ymer.

The only seed to advance to the semis was 15th seed Carlos Alcaraz, who saw off Marcos Giron.

Pablo Carreno Busta sailed into the quarter-finals of the Winston-Salem Open an the top seed was joined by Richard Gasquet.

Carreno Busta – the 2016 champion – was too good for Dominik Koepfer 6-2 6-3 at the ATP 250 tournament on Wednesday.

The Spaniard, who stunned world number one Novak Djokovic to win bronze at the Olympic Games, will meet Ilya Ivashka, who upstaged ninth seed Jan-Lennard Struff 6-2 6-1.

"It was a very good match. I think I played very aggressively today, I made a lot of winners," Carreno Busta said. "I played against him the last two tournaments so it was important to me at the beginning of the match to be very focused and play very aggressive so I think this was a very good match for me.

"I'm feeling really comfortable playing this year, also. We know next we have the US Open but day by day I need the confidence, I need the rhythm. I think that I'm playing at a really good level so I would like to continue this way."

Former world number seven Richard Gasquet saw off third seed Daniel Evans 6-4 7-6 (7-4), Frances Tiafoe defeated Thiago Monteiro 7-5 7-6 (7-2), while fourth seed Marton Fucsovics was sent packing by Carlos Alcaraz 6-3 0-6 6-2.

Lucas Pouille continues to build momentum at the Winston-Salem Open after overcoming veteran Feliciano Lopez in straight sets.

Pouille was on the brink of elimination in qualifying after facing match point before booking his spot in the main draw.

Now, the Frenchman is preparing for the second round following his 6-1 6-4 victory over Lopez on Monday.

Pouille saved all four break points he faced as the former world number 10 claimed his first ATP Tour-level victory since April's Monte Carlo Masters.

Awaiting Pouille in the second round is third seed Daniel Evans, who received a bye in the opening round.

As for 14th seed Richard Gasquet, he prevailed 7-6 (7-4) 7-6 (8-6) against Egor Gerasimov at the ATP 250 event.

Elsewhere, Federico Coria and Jordan Thompson were among the players to progress.