Serbia's top-seeded Novak Djokovic overcame a brief bout of nerves in the second set before beating 14-times French Open champion Rafael Nadal 6-1, 6-4 at the Paris Olympics on Monday and moving into the third round.

While Djokovic remains in the hunt for his elusive Olympic gold, Spain's Nadal now has only the doubles competition left to add to his two Olympic gold medals, partnering Carlos Alcaraz.

Djokovic led 6-1, 4-0 before a Nadal comeback attempt that saw him briefly level 4-4.

"I was just very proud to be part of this match and ... I wanted to do my job on the court and really execute the game plan as much as I possibly can," Djokovic said.

"So almost a perfect match, the 6-1, 4-0. Then things got complicated, I started to hesitate a little bit on my shot he stepped in, the crowd got involved and for all, it was really anybody's set, anybody's game. Just very glad to overcome this incredible challenge."

Women's world number one Iga Swiatek of Poland had an even easier morning, crushing France's Diane Parry 6-1, 6-1 to book her own third round spot.

Czech Barbora Krejcikova, the newly crowned Wimbledon champion, also advanced with a straight sets victory over China's Wang Xinyu as did American Coco Gauff, beating Argentine Maria Lourdes Carle 6-1, 6-1.

But all eyes on Monday were on the Nadal-Djokovic showdown with the crowd desperate to see the world's best clay-court player make one last one run in Paris even though his best playing days are long behind him.

"I was not able to put him in difficult positions," Nadal said. "I was not able to have enough quality shots, enough quality of movements. Playing against Novak without creating damage to him and without having the legs of 20 years ago is almost impossible."

At age 37, Djokovic, who has won 24 Grand Slam singles titles to Nadal's 22, has remained far more competitive than his injury-plagued opponent. He left nothing to chance in a flawless display over a set and a half.

The world number two stretched the 38-year-old Spaniard with punishing groundstrokes and perfect drop shots, making him look his age as he raced through the first set and went 4-0 up in the second.

The crowd, ready for a mouth-watering epic on their record-extending 60th encounter, instead were being treated to what looked like a fast-track Djokovic win.

Nadal, with his thigh strapped due to a recent injury, was spilling unforced errors across Court Philippe Chatrier, lacking precision and consistency.

With the crowd sensing the end of an era was fast approaching, Nadal was desperate to avoid one of the most bruising defeats of his career on his favourite clay surface.

A Djokovic double fault saw Nadal pull back to 4-2 and that was celebrated like a victory with almost the entire stadium jumping from their seats to cheer him on.

After another two games the Spaniard was level but it was nothing more than a brief reprieve as Djokovic sealed victory on his first match point with an ace.

Alcaraz eases into third round

Meanwhile, Spain's Carlos Alcaraz defeated the Netherlands's Tallon Griekspoor 6-1, 7-6(3) to also reach the third round, showing the form that will make him hard to beat but also some sloppiness as he strives for Olympic gold.

The world number three, who won this year's French Open and Wimbledon titles was back on Court Philippe-Chatrier and set the tone from the start with an ace and two forehand winners.

With the crowd having seen fellow-Spaniard Nadal beaten by Djokovic, Alcaraz appeared determined to show he was ready to take up the baton at Roland Garros, breaking Griekspoor immediately and racing through the first set in 32 minutes.

But the Dutchman, ranked 28 in the world, made a better fist of it in the second set. He repeatedly held his serve under pressure, giving back as much as Alcaraz threw at him and at times forcing the Spaniard into some uncharacteristic errors.

The set went to a tiebreak with the 21-year-old Alcaraz stepping up the pace and showing subtlety to win the match.

In the third round he will play Russian Roman Safiullin, the world number 67, who is competing as a neutral athlete.

• THE OLYMPICS, 2024