World number one Djokovic, who will hold all four Grand Slam titles for the second time in his career if he wins the tournament, beat Poland's Hubert Hurkacz 6-4, 6-2, 6-2 on Philippe Chatrier court.

Earlier in the day, defending champion Nadal defeated German qualifier Yannick Hanfmann 6-2, 6-1, 6-3.

Nadal is chasing a record-extending 12th title at Roland Garros.

Next up for the 17-time Grand Slam champion is another German qualifier, Yannick Maden.

Awaiting Djokovic, a 15-time Grand Slam winner, in the second round is Switzerland's Henri Laaksonen.

Among the other players advancing was Switzerland’s Stan Wawrinka, the 2015 champion, who overcame Slovakia's Jozef Kovalík 6-1, 6-7, 6-2, 6-3.

The most notable casualty from the men’s singles draw was 12th seed Daniil Medvedev after the Russian surrendered a two-set lead to lose 6-4, 6-4, 3-6, 2-6, 5-7 to world number 43 Pierre-Hugues Herbert of France.

Also crashing out was 15th-seeded Georgian Nikoloz Basilashvili following a 4-6, 1-6, 3-6 loss at the hands of world number 78 Juan Ignacio Londero of Argentina.

In the women's singles, former world number one Caroline Wozniacki of Denmark suffered a shock three-set defeat against world number 68 Veronika Kudermetova in the first round. 

Wozniacki, a quarter-finalist at Roland Garros in 2010 and 2017, was beaten 6-0, 3-6, 3-6 by the Russian debutant.

"I played really well in the first set – I played aggressive, I played the way I wanted to play," Wozniacki, the 2018 Australian Open champion, told Sky Sports.

"And then I think she got very lucky at the start of the second set and took advantage of the opportunities she got. 

"I think I just lost a little steam in the end."

Kudermetova will meet world number 99 Zarina Diyas of Kazakhstan in the second round after she defeated France's Audrey Albie 6-2, 6-2.

Two-time Wimbledon champion Petra Kvitová of Czech Republic withdrew from the tournament just hours before her scheduled match against Romania's Sorana Cîrstea due to an injury to her forearm.

Slovenia's Kaja Juvan replaced Kvitová in the draw but she lost 7-5, 4-6, 5-7 to Cîrstea.

Elsewhere, fourth seed Kiki Bertens of The Netherlands overcame France's Pauline Parmentier 6-3, 6-4, while eighth seed Ashleigh Barty of Australia claimed a 6-3, 6-3 win over the United States' Jessica Pegula.