Novak Djokovic celebrates winning his match against Alexandre Muller in New York on Tuesday. AP

Novak Djokovic ensured he will return to the top of tennis's world rankings with an emphatic first round victory at the US Open on Monday as women's world number one Iga Swiatek and American rival Coco Gauff advanced.

Djokovic, chasing a record-extending 24th Grand Slam singles title in New York, shrugged off a late-night start on the Arthur Ashe Stadium to demolish France's Alexandre Muller 6-0, 6-2, 6-3 in just 1hr 35min.

The win means Djokovic is guaranteed to replace defending US Open champion Carlos Alcaraz as world number one when the tennis rankings are next updated after the tournament.

Djokovic is playing in New York for the first time since suffering an agonising defeat in the 2021 final in New York.

He was barred from entry to the United States in 2022 for his refusal to get vaccinated against Covid-19, meaning he was unable to play the US Open.

On Monday the 36-year-old played like a man making up for lost time, reeling off 32 winners and breaking Muller eight times in a lopsided encounter that finished at around 12.40am local time.

Djokovic, who will face Spain's Bernabe Zapata Miralles in the second round, said he was unfazed by the late start to his game.

"I didn't care if I started after midnight because I was looking forward to this moment for few years, to be out on the biggest stadium in our sport, the loudest stadium in our sport, playing night session," Djokovic said. "It was a great joy to be stepping out on the court.

'Flawless' tennis

"I think the performance explains how I felt tonight, particularly in the first two sets. It was kind of lights-out tennis really, almost flawless, perfect first set.

"Overall I'm very, very pleased with the way I feel, with the way I'm playing. Hopefully I can maintain that level."

Novak Djokovic reaches of a shot against Alexandre Muller during their Men's Singles First Round match. AFP

Djokovic's arrival on court had been delayed after a gruelling three-set battle between American teenager Gauff and Germany's Laura Siegemund in the preceding night game.

The 19-year-old Gauff, tipped by many as the biggest threat to defending US Open champion Swiatek, was forced to dig deep before winning 3-6, 6-2, 6-4 in 2hr 50min.

An ill-tempered clash was marked by tetchy confrontations by both players with chair umpire Marijana Veljovic.

Gauff accused the Serbian official of failing to properly enforce time violation rules against Siegemund.

"I felt like the rules were being bent," Gauff said. "That's why a lot of players get mad when these time violations are called because one ref is letting them go over, the other is more strict on the time."

Siegemund, 35, meanwhile voiced disgust at the partisan New York crowd, describing them as "respectless" for the way they cheered every error or missed first serve.

"They had no respect for me, no respect for the way I played, no respect for the player that I am, they had no respect for good tennis," Siegemund said.

Agence France-Presse