Serena Williams' latest quest for a record-equalling 24th Grand Slam title ended with a 6-3, 7-5 defeat by Kazakh 21st seed Elena Rybakina in the French Open last 16 on Sunday.

Iga Swiatek kept her bid alive to become the first woman since Mary Pierce in 2000 to win the French Open singles and doubles title at the same tournament, saving seven match points with partner Bethanie Mattek-Sands to reach the quarter-finals.

Former world number one Roger Federer, who is targeting a record 21st Grand Slam title at Wimbledon, withdrew from the French Open on Sunday, a day after winning a tough third-round match, opting to save himself for the grass-court season.

Roger Federer said Sunday he is considering withdrawing from the French Open despite reaching the fourth round as Novak Djokovic and Rafael Nadal set up clashes with two Italian teenagers widely seen as their Grand Slam heir apparents.

World number one Novak Djokovic booked his spot in the second week of the French Open with a dominant 6-1, 6-4, 6-1 third-round win over 93rd-ranked Lithuanian Ricardas Berankis on Saturday.

Claycourt machine Rafa Nadal celebrated his 35th birthday by handing his longtime pal Richard Gasquet a 6-0 7-5 6-2 masterclass as he stormed into the third round of the French Open on Thursday.

World number one Novak Djokovic on Tuesday hailed Naomi Osaka as "brave and bold" for withdrawing from the French Open after revealing her struggles with depression and anxiety.

Rafael Nadal fought back from 2-5 down in the third set to ensure he started his bid for a 14th French Open title with a comfortable victory over Alexei Popyrin on Tuesday.

Petra Kvitova has withdrawn from the French Open after injuring her ankle in a freak fall while performing her post-match media duties on Sunday, the 11th seeded Czech player said in a statement.

Japan joined leading figures in tennis in rallying around Naomi Osaka on Tuesday after the world number two withdrew from the French Open in a row about post-match media duties, saying she had been suffering from "depression" and "anxiety".

Naomi Osaka was fined $15,000 by Grand Slam organisers for boycotting a news conference following her first-round win and the world number two was also warned of possible expulsion from Roland Garros and future majors if she fails to meet her media commitments.

World number two Naomi Osaka began her French Open campaign with a 6-4, 7-6(4) win over Romanian Patricia Maria Tig on the opening day of the claycourt Grand Slam yesterday.

Rafael Nadal and Novak Djokovic will set their sights on more Grand Slam history at the French Open as Roland Garros embraces a new but eerily empty era of night time tennis.

While fans and pundits continue to debate who should be considered the greatest men's tennis player of all time, 23-times Grand Slam winner Serena Williams says Roger Federer gets her vote.

World number one Novak Djokovic took a swipe at all the talk about the younger generation of tennis players, saying rival Rafael Nadal and himself were the 'Next Gen'.

Rafa Nadal warmed up for the French Open with a battling 7-5 1-6 6-3 win over world number one Novak Djokovic as the Spaniard claimed a record-extending 10th Italian Open title in Rome on Sunday in the latest chapter of their rivalry.

French Open champion Iga Swiatek served a warning to her rivals ahead of the claycourt Grand Slam with a 6-0 6-0 demolition of former world number one Karolina Pliskova in the Italian Open final on Sunday

Nine-time champion Rafael Nadal dispatched his Madrid Masters slayer Alexander Zverev 6-3, 6-4 to reach the Italian Open semi-finals on Friday.

World number one Novak Djokovic's quarter-final match against Stefanos Tsitsipas has been pushed back until Saturday after play was suspended because of rain on Friday.

Top seeds Novak Djokovic and Rafael Nadal reached the quarter-finals of the Italian Open along with another former winner Alexander Zverev on Thursday as spectators returned to the stands for the first time in Italy.