World number one Naomi Osaka survived another major scare to reach the third round of the French Open.

The 21-year-old, who is chasing a third consecutive grand slam title, lost the first set 6-0 against Anna Karolina Schmiedlova on Tuesday and was two points from defeat.

Things did not get quite so hairy against former world number one Victoria Azarenka in a high-quality match but the top seed was a set and a break down before recovering to win 4-6 7-5 6-1.

Osaka, who said she had never been more nervous during a match than against Schmiedlova, again made a poor start, with Azarenka winning the first four games.

Two-time Australian Open champion Azarenka has been getting closer to her best form having finally returned full-time to the tour last spring following a bruising custody battle over her toddler son.

She weathered an Osaka fightback to take the opening set, the pair trading ferocious ground strokes, and then opened up a 4-2 lead in the second.

But Osaka has established a reputation as one of the toughest players mentally and she dug her way back into the match before racing out to a 5-1 lead in the decider.

Azarenka put up more resistance at the end but ultimately Osaka was just too strong.

Serena Williams cruised past Kurumi Nara

Serena Williams breezed into the next round with a routine 6-3 6-2 win against Japanese Kurumi Nara, wasting no energy in her quest for a record-equalling Grand Slam singles title.

The 10th seed, chasing a first major since the 2017 Australian Open, survived a first-set fright in her opening match, but there was no hiccup this time.

She will take on fellow American Sofia Kenin in the next round, with world number one Naomi Osaka a potential opponent in the quarter-finals.

Osaka next faces Katerina Siniakova, who knocked out 29th seed Maria Sakkari, while Williams takes on young American Sofia Kenin.

Defending champion Simona Halep was taken to three sets for a second successive match, this time by Pole Magda Linette, before coming through 6-4 5-7 6-3.

Halep looked to be in control at a set and 5-3 and held three match points but Linette fought back to force a decider. Halep then missed another chance to serve for the match at 5-2 but clinched it moments later.

Halep revealed she is struggling with illness, saying: "I didn't feel that great. I'm a little bit sick. I'm really happy I could fight until the end and win this difficult match."

There were standout victories, meanwhile, for two 17-year-olds, with Amanda Anisimova repeating her Australian Open triumph over Aryna Sabalenka and Wimbledon junior champion Iga Swiatek knocking out 16th seed Wang Qiang.