The WTA and ATP Tours have been suspended until July 13 due to the COVID-19 pandemic, with Wimbledon called off for the first time since 1945.
French Open organisers announced that the clay-court major would be put back to September 20, just a week after the US Open is scheduled to finish.
Martic, currently in lockdown in Miami, says featuring in two grand slams in quick succession would be far from ideal, but the world number 15 would embrace that challenge as an alternative could be no more tennis this year.
The Croatian told Stats Perform: "That's going to be a very unusual situation [playing the French Open so soon after Flushing Meadows] but like we all know, the schedule is not going to be perfect as there are too many tournaments.
"Everything will be cramped up, we will be flying a lot, changing surfaces and time zones. Things are definitely not going to be ideal, but grand slams are what we play for and if we get a chance to play two this year that would be great.
"Everybody fears the season could be over, they are trying their best to put potential schedules together but we have to see if anything can happen.
"If the situation in the world gets better and we are able to play, I would definitely love to play two [majors]."
Martic, who has trained every day since arriving in Florida, accepts she cannot make any plans in such an unprecedented situation.
The 29-year-old added: "My favourite part of the year is being in Europe, playing on clay is always fun and I really enjoy it but this all came so suddenly, it's a weird situation.
"When you stop it's usually because something hurts, so this waiting is not fun, but it is what it is.
"I can do everything I need to be doing, it's just you don't know how to plan things and how hard to work out, it's hard to plan anything right now."
Martic, the top seed at the WTA International event that marks the return of the Tour amid the coronavirus pandemic, overcame Liudmila Samsonova 5-7 6-4 6-2.
Croatian Martic, the world number 15, needed two and a half hours to get past the qualifier in Italy on Thursday.
She will face Aliaksandra Sasnovich in the last eight.
Kontaveit was also pushed before recording a 3-6 6-2 6-2 victory over Laura Siegemund.
Yastremska and Camila Giorgi will meet in a quarter-final after respective wins over Oceane Dodin and Kaja Juvan.
Talented Ukrainian seventh seed Yastremska was too good for Dodin 6-2 6-4, while Giorgi beat Juvan 3-6 6-2 6-4.
Top seed Martic battled past qualifier Aliaksandra Sasnovich 7-6 (7-5) 7-6 (7-3) in their quarter-final.
The Croatian converted four of seven break points and saved seven of 11 to advance at the WTA International event, which marks the first tournament back after the coronavirus-enforced break.
Martic will meet Kontaveit, who beat teenage wildcard Elisabetta Cocciaretto 6-1 4-6 6-1.
Unseeded pair Camila Giorgi and Fiona Ferro will meet in the other semi-final.
Giorgi got past seventh seed Dayana Yastremska 4-6 7-6 (7-5) 6-3 after saving two match points, while Ferro brushed past Italian veteran Sara Errani 6-4 6-1.
The 21-year-old, who is set to reach a personal high of 31 in the world rankings on Monday, saw off her Croatian opponent in just an hour and 16 minutes, winning 6-3 6-1.
Potapova dropped as low as 124 in the rankings last year, but this week's success is another reminder of the Russian's promise.
Martic seemingly represents something of a good luck charm for Potapova – she also beat her en route to her first ever WTA title last year in Istanbul.
It did not always look like going in Potapova's favour, though, as she was broken right at the start and then only just held off Martic in her second service game.
Potapova then secured two breaks that helped her seal the first set, and after Martic won the first game of the second, the eventual champion reeled off six on the bounce to emphatically romp to victory.
The Kazakh Putintseva struggled to get going, failing to convert any of her seven break points, as the Serbian Krunic broke her serve four times en route to a 6-2 6-2 win.
Bernarda Pera will await Krunic in the final in Hungary, after her 6-3 6-4 victory over Anna Bondar.
Bondar raced out to an early 3-0 lead in the first set, but Pera rattled off six games in a row to take the opener.
The Croatian-born American then won the first three games of the second set, before overcoming a desperate late Bondar charge to break her at 5-4 and finish things off.
Sunday's final will be the third meeting between Krunic and Pera with the latter winning both of the previous contests, firstly in the quarter-finals of the Guangzhou Open in 2018 and then in Moscow in 2021.
At the Ladies Open Lausanne, qualifier Olga Danilovic cruised through to the final with a 6-3 6-2 victory over Russian Anastasia Potapova.
Danilovic won her first WTA Tour singles event in Moscow in 2018, overcoming Potapova after three sets.
And the world number 124 was victorious against Potapova once more in Switzerland to seal her place in her second WTA Tour singles final.
The Serbian 21-year-old will meet Petra Martic in the decider on Sunday after Martic overcame sixth seed Caroline Garcia 6-4 1-6 6-3.
Neither player had dropped a set on their way to the semi-finals, but things at Lausanne were tied up at one set each after two.
Garcia had won all three of her previous meetings with Martic, but the Croatian's two crucial breaks of serve in the final set were telling, as she held her nerve to reach the final against Danilovic.
A 6-4 1-6 7-5 victory for Madison Keys over top seed Sabalenka capped a day of upsets in Berlin.
American Keys fought back from a set down to bundle the world number four out in an hour and 29 minutes.
The battling Sabalenka saved 10 break points but was unable to avoid an early exit in the inaugural grass-court event.
Second seed Svitolina started her grass-court season with a 6-4 7-5 defeat to Ekaterina Alexandrova.
Russian Alexandrova fended off seven set points in the second set before sending the world number six, who was given a first-round bye, packing.
Svitolina, playing her first match since crashing out of the French Open in the third round, became the fourth top-10 scalp for Alexandrova, who will face Belinda Bencic in her fifth quarter-final of the year.
Andreescu's first match on grass since Wimbledon qualifying three years ago ended in a 7-6 (7-2) 7-5 loss to Alize Cornet.
The third seed from Canada parted with her long-time coach Sylvain Bruneau after she was beaten by Tamara Zidansek in the first round at Roland Garros and was unable to hit the ground running on grass.
Bencic, the fifth seed, advanced with a 6-3 5-4 success over Petra Martic.
Sakkari beat world number five Svitolina 6-3 6-3 to progress to the last eight of a WTA Premier event for the third time this season.
Unseeded Greek Sakkari struck 32 winners and returned superbly, winning all but eight of 29 points on Svitolina's second serve.
The 23rd-ranked Sakkari will face either wildcard Jelana Ostapenko or Ons Jabeur for a place in the semi-finals.
Ostapenko knocked out fifth seed Petra Martic, the 2017 French Open champion easing to a 6-3 6-1 victory.
Martic had won their previous two meetings, but the Croatian was beaten in just 57 minutes at the indoor hard-court event.
Anett Kontaveit was another seed to fall, Sara Sorribes Tormo reaching a maiden Premier-level quarter-final at the expense of the Estonian with a 6-1 6-4 success.
Victoria Azarenka is also two wins away from the final, coming from a set down to see off Barbora Krejcikova 2-6 6-2 6-1, and will now face Karolina Muchova or Elise Mertens, who got past Amanda Anisimova in straight sets.
Williams had taken up a wildcard to play in the tournament following an early exit in Rome, where she was beaten by Nadia Podoroska in her opening contest in the clay-court swing.
Her campaign in Parma got off to a better start on Monday, a 6-3 6-2 result against WTA Tour debutant Lisa Pigato bringing a first triumph since losing in the semi-finals of the Australian Open in February.
However, the 23-time grand slam champion was unable to repel a determined Siniakova as she slipped out at the last-16 stage.
"It was a fantastic match and I played so well, I'm so happy that I could finish like that," Siniakova said after recording a 7-6 (7-4) 6-2 result.
"It was a pleasure to share the court with her.
"Now I will have the pressure because I defeated a great player, but I will enjoy it. I'm happy that I can continue and I will try to play my best in the next match."
Having failed to convert a set point opportunity, Williams hit back after losing serve with a break of her own to force a tie-break in the opener.
But Siniakova forced her way into a 5-3 lead before sealing it with a service winner, then quickly seized control of proceedings in a second set which was far less competitive.
Third seed Coco Gauff came through two tie-breaks to see off Kaia Kanepi, the American teenager having let slip a 5-1 lead in the second set before eventually sealing a 7-6 (8-6) 7-6 (9-7) win.
Petra Martic had no such issues in her opening contest against Varvara Gracheva, the second seed easing through 6-4 6-2 after one hour and 21 minutes on court.
Williams and Halep played in an exhibition event with a crowd of 4,000 watching on in Adelaide last Friday and they were back in competitive action three days later.
Legendary American Williams beat Daria Gavrilova 6-1 6-4 to move into the third round of the Yarra Valley Classic.
The fifth seed struck 27 winners to 15 unforced errors on Margaret Court Arena as she set up a meeting with Tsvetana Pironkova, who ousted Donna Vekic 1-6 6-4 6-2.
Williams said: "It was a good match for me. It wasn't easy at all. It was lots of rallies and lots of movement, and she's from here, so she obviously always plays hard. So it was really good and it felt good to clinch that in the end."
Third seed Karolina Pliskova, Petra Martic, Danielle Collins and Marketa Vondrousova also advanced to the last 16 on Monday.
Elsewhere, top seed Halep is through to the third round of the Gippsland Trophy following a 6-4 6-4 win over Anastasia Potapova.
Halep hit 23 winners and broke twice in each set in what was her first official match since October.
Elina Svitolina, the third seed, beat Andrea Petkovic 6-1 6-4, while Coco Gauff, Ekaterina Alexandrova and Jelena Ostapenko were among the other winners seven days prior to the start of the first grand slam of 2021.
Swiatek, who became the first female player to win 25 consecutive matches since Serena Williams in 2015, will face Bianca Andreescu in the last eight after she eased past Petra Martic 6-4 6-4.
"I didn't start well, and everybody could see that," Swiatek told reporters. "I'm really happy with the way I reacted and how I improved in the first set.
"Also how different the second set looked to the first one because I could really reset and really change the way I played. That's the most positive thing for me."
There was a shock in the final game of the day, though, as Daria Kasatkina dumped out number two seed Paula Badosa 6-4 6-4.
Third seed Aryna Sabalenka sealed a third straight win over Jessica Pegula, easing to a 6-1 6-4 victory, while fourth seed Maria Sakkari defeated Coco Gauff 6-4 7-5.
Seventh seed Danielle Collins was knocked out by unseeded compatriot Amanda Anisimova, the 20-year-old cruising past the Australian Open finalist 6-2 6-2.
There were also victories for Jil Teichmann, who overcame Elena Rybakina 6-7 (3-7) 6-3 7-5, and ninth seed Ons Jabeur, who beat Yulia Putintseva 6-3 6-2.
Poland trailed after Lorenzo Musetti and Matteo Berrettini secured wins against Daniel Michalski and Hubert Hurkacz respectively, only for Swiatek and Magda Linette to level things with respective singles victories over Martina Trevisan and Lucia Bronzetti.
That sent the Brisbane city final to a decider in the mixed doubles, which Swiatek and Hurkacz won with ease 6-1 6-2 against Musetti and Camilla Rosatello, though there was a pause in the second set to dry rainfall on the court.
Despite defeat, Italy also advanced to the final four as the city finals loser with the best record.
It was more routine in Sydney as the United States eased to a 4-1 win against Great Britain.
Madison Keys came from a set down to beat Katie Swan, while Jessica Pegula eased past Harriet Dart 6-2 6-0 after Cameron Norrie had defeated Taylor Fritz in three sets.
Despite going a set behind, Frances Tiafoe came back to beat Dan Evans 3-6 7-5 6-3 to clinch the win for his country, before Pegula and Fritz added some gloss after beating Dart and Evans in the mixed doubles.
The third city final in Perth included a thriller as Greece's Stefanos Tsitsipas beat Borna Coric 6-0 6-7 (4-7) 7-5. Donna Vekic had no trouble getting Croatia on the board as she eased past Despina Papamichail 6-2 6-0.
Maria Sakkari put Greece 2-1 ahead when she beat Petra Martic 6-3 6-3, but Borna Gojo defeated Stefanos Sakellaridis in straight sets to make it 2-2.
However, Greece secured the win and their place in the last four after the pairing of Sakkari and Tsitsipas saw off Martic and Gojo 7-6 (8-6) 6-4.
Greece will take on Italy in the semi-finals, while Poland face the USA, with both taking place in Sydney on Friday.
The Polish teenager began her day with a 6-2 7-5 morning victory over fifth seed Svitolina, twice a winner of this tournament in Rome.
It was a match that was carried over from Friday's schedule after rain interrupted play, and Swiatek delivered a convincing performance.
That set up the semi-final clash with Gauff, the 17-year-old American who was competing at this stage of a WTA 1000 event for the first time, having been gifted her last-four place when Ash Barty abandoned their quarter-final match due to injury on Friday.
There was no sign of fatigue from Swiatek as the 19-year-old powered to a 7-6 (7-3) 6-3 victory in a battle of the leading teenage stars of the women's game, who faced each for the first time in what could be a long rivalry.
Swiatek said: "I felt really good today. It's a big difference between my previous matches and today. I was able to beat Elina, so that shows that my game is here, I'm ready for anyone. It gave me a real confidence boost."
Quoted on the WTA website, the 15th seed added: "It's always hard to play against a young superstar, especially when I'm not used to that because I was always the youngest one.
"I just tried to have a high level of energy, even though it was my second match."
Between her two matches, Swiatek would have learned it was Pliskova waiting in the final, as the Czech ninth seed defeated Croatian Petra Martic 6-1 3-6 6-2 to keep up her remarkable record in the Italian capital.
Pliskova won the Rome title in 2019 and was runner-up to Simona Halep last year, but the 29-year-old former world number one has not been to a final since this event unusually took place in September of last year, having been delayed due to the pandemic.
Swiatek won as a major outsider at Roland Garros in October, defying her world ranking which at the time was a lowly 54th, and will face, in Pliskova, a player who has yet to win a grand slam title, a glaring absence amid an otherwise stellar career.
Against Gauff, Swiatek made 25 winners and just 16 unforced errors, a healthy ratio, and took three of her four break-point opportunities.
She sealed victory on a third match point, a big backhand forcing a stretching Gauff to chip beyond the baseline.
Gauff hit seven aces but also five double faults and had 33 winners and 32 unforced errors in the contest.
Osaka, the 2018 champion in New York, was pushed before getting past Ukrainian teenager Marta Kostyuk.
The top half of the women's draw is packed with seeds as Kerber and Kvitova were among those advancing at Flushing Meadows.
Petra Martic, the eighth seed, also booked her spot in the fourth round.
OSAKA GETS THROUGH TEST
Osaka, the fourth seed and two-time grand slam winner, battled past Kostyuk 6-3 6-7 (4-7) 6-2.
The Japanese star had 30 winners and 38 unforced errors before advancing in two hours, 33 minutes.
Osaka's left leg was again heavily strapped, but the 22-year-old insisted she was feeling fine.
"I felt like I was moving well," she said. "It could be better, but I think for a three-set match, the amount of movement that I did, and the fact that I felt like I could have kept going if I really needed to is definitely a good sign."
Awaiting Osaka in the fourth round is Anett Kontaveit after the Estonian 14th seed powered past Magda Linette 6-3 6-2.
KERBER, KVITOVA KEEP WINNING
For the first time since winning the tournament in 2016, Kerber is into the fourth round.
The German 17th seed was too good for Ann Li 6-3 6-4 in just 76 minutes.
"I came here and I have no idea where I am, to be honest. Still, I mean, I had three good matches, also close matches. Every match was a little bit different," Kerber said.
"But now the second week and the fourth round, I mean, you know, I'm not thinking too much ahead. It's more like I have a day off tomorrow. Then I have the next match. This is more my focus.
"I'm really trying to staying here as well in the bubble, also mentally and getting ready for the next match."
Up next for Kerber is Jennifer Brady, the American 28th seed having recorded a 6-3 6-3 win over Caroline Garcia.
A two-time US Open quarter-finalist, Kvitova advanced after a 6-4 6-3 victory over Jessica Pegula on Arthur Ashe Stadium.
MARTIC CONTINUES RUN
A quarter-finalist at the French Open last year, Martic matched a career best thanks to a 6-3 6-3 win over Varvara Gracheva.
The Croatian is into the fourth round in New York for just the second time, having also achieved the feat last year.
She will meet Yulia Putintseva, who overcame Aliaksandra Sasnovich 3-6 6-2 6-1.
The world number one, who has never previously gone beyond the quarter-finals at SW19, was a 6-4 6-3 victor in one hour and 20 minutes on Centre Court.
Martic held her own until the 10th game of the opening set but the first break point she gave up was converted by Swiatek, who came through strong pressure in several games on her own serve.
The second set followed a similar pattern, Swiatek needing two break points this time as she made the breakthrough eight games in.
Martic was a beaten player from there as Swiatek served out her final game to love, a crashing forehand winner teeing up three match points, and a big serve on the first giving world number 79 Martic no chance.
Data Debrief: Swiatek replicates Serena run
Swiatek has now won 21 consecutive matches as world number one, the longest such streak by any player on the WTA Tour since Serena Williams had an identical run between the 2014 WTA Finals and the 2015 Madrid Open.
She has also made at least the round of 32 at 18 consecutive grand slams.
In the Open Era, only Martina Navratilova (35), Conchita Martinez (30), Arantxa Sanchez Vicario (25) and Steffi Graf (19) have ever done so at more majors in a row.
