Novak Djokovic feels ready to go "deep into the tournament" after coasting to a straight-sets first-round win over Mikael Ymer at the French Open.

The world number one produced a composed display to see off the 22-year-old Swede in his return to grand slam action following a shock disqualification from the US Open for accidentally hitting a line judge with a ball he had struck away in annoyance.

Djokovic, who won the Italian Open title in Rome last week, eased through the first set in just 20 minutes under the roof on Court Philippe Chatrier before wrapping up a 6-0 6-2 6-3 victory.

Djokovic will go on to face Lithuania's Ricardas Berankis in round two.

The world number one maintains he is fully focused on the challenges ahead, rather than the fall-out from events at the US Open.

"I have not had any traces of New York in my mind. I'm over it. Honestly forgot about it, I'm not thinking about it," Djokovic said.

"I thought I started off extremely well, winning 6-0 first set is the best possible way to start a Grand Slam.

"This is exactly what my intentions will be, trying to get off the blocks very strong with a good intensity."

Elsewhere on Tuesday, number 13 seed Andrey Rublev recovered from two-sets down to beat American Sam Querrey.

The Russian, who won the final of the Hamburg Open on Sunday, came through 6-7 (5) 6-7 (4) 7-5 6-4 6-3 in a match which lasted almost three-and-a-half hours.

Italian seventh seed Matteo Berrettini beat Canada's Vasek Pospisil 6-3 6-1 6-3, Chile's Christian Garin, seeded number 20, defeated Philipp Kohlschreiber 6-4 4-6 6-1 6-4 and Australian Marc Polmans ended the hopes of home player Ugo Humbert with a 6-2 6-2 3-6 6-3 win.

Number 22 seed Dusan Lajovic progressed after a 6-4 7-6 (4) 4-6 6-1 victory over Gianluca Mager while South African Kevin Anderson is also into the second round following his 6-2 6-3 6-4 win over Laslo Djere.

In Tuesday's later matches, world number six Stefanos Tsitsipas survived a scare as he fought back from two-sets down to defeat Jaume Munar 4-6 2-6 6-1 6-4 6-4.

The Greek, runner-up to Rublev in Hamburg, produced a string of unforced errors as the 109-ranked Spaniard took control of the match before digging deep to mount a strong recovery.

There was more disappointment for the few French fans at the Paris venue as Gilles Simon was beaten 6-2 7-5 5-7 6-3 by Canada's Denis Shapovalov and number 10 seed Roberto Bautista Agut defeated Richard Gasquet 7-6 (5) 6-2 6-1.

Grigor Dimitrov, the 18th seed, progressed with a 6-3 6-2 6-2 win over Gregoire Barrere.