Defending women's singles champion Świątek played the first match on the main court at the United States Tennis Association Billie Jean King National Tennis Center in New York City, and dropped just one game in a 6-0, 6-1 victory against world number 86 Rebecca Peterson of Sweden.

"I'm happy that I could play such a great game, and with all the pressure and expectations, that I can just have fun on court," Świątek said.

Australia's Daria Saville is due to be her opponent in the second round after a comfortable 6-0, 6-2 win against home wildcard Clervie Ngounoue.

The first day produced a 6-2. 6-1 victory for Kazakhstan's world number four Elena Rybakina against Marta Kostyuk of Ukraine, and in the other match on Arthur Ashe, world number six Coco Gauff of the US came from a set down to beat German qualifier Laura Siegemund 3-6, 6-2, 6-4.

Russia's 16-year-old sensation Mirra Andreeva, competing as a neutral due to the war in Ukraine, is set to be her next opponent after coming from behind to defeat Australia's Olivia Gadecki 1-6, 6-3, 6-4.

In her first Grand Slam appearance since returning from her 2020 retirement, two-time finalist Caroline Wozniacki emerged victorious with a 6-3, 6-2 victory against another Russian neutral, Tatiana Prozorova, on Louis Armstrong Stadium.

Three-time finalist Victoria Azarenka, a Belarusian also competing as a neutral, was among the other winners 6-1, 6-2 against French wildcard Fiona Ferro.

Olympic champion Belinda Bencic of Switzerland beat Kamilla Rakhimova, another Russian competing under a neutral flag, 6-2, 6-4.

The eighth seed Maria Sakkari of Greece was the most notable player to exit on day one, losing 6-4, 6-4 to Spain's Rebeka Masarova.

It has been a disappointing season for Sakkari, knocked out in the first round of the last three Grand Slams.

In the men's singles, Djokovic's return to the US Open after his absence last year due to a refusal to get vaccinated against COVID-19 began with a routine 6-0, 6-2, 6-3 victory against France's Alexandre Müller.

"It’s been a couple of years and to come in front of you guys is always a pleasure and an honour to play on Arthur Ashe," Djokovic told the crowd afterwards.

Djokovic has won the US Open three times, although not since 2018, and his recent appearances included a fourth-round disqualification for accidentally striking a line official with a ball not in play in 2020 and a defeat to Russia's Daniil Medvedev in the 2021 final to deny him a "golden slam" of all four major titles during the year.

After wins at the Australian Open and French Open this year, his hopes of a golden slam for 2023 were ended with a defeat to Spain's world number one Carlos Alcaraz in the Wimbledon final, his first defeat at the grass-court Grand Slam since 2017.

His first-round victory means he is set to return to the top of the Association of Tennis Professionals men's singles rankings after the US Open.

America's 10th seed Frances Tiafoe was the other winner on Arthur Ashe Stadium, beating compatriot Learner Tien 6-2. 7-5, 6-2.

The 2022 finalist and fifth seed Casper Ruud of Norway came through 7-6, 3-6, 6-4, 7-6 against American qualifier Emilio Nava, but fourth seed Holger Rune of Denmark suffered a surprise exit 6-3, 4-6, 6-3, 6-2 to Spain's Roberto Carballés Baena.

Canada's Félix Auger-Aliassime was another high-profile player to lose in the first round, going down 7-6, 4-6, 6-1, 6-4 against American Mackenzie McDonald.

Greece's seventh seed Stefanos Tsitsipas beat Canada's Milos Raonic 6-2, 6-3, 6-4 in straight sets, and the 2020 winner Dominic Thiem of Austria, who has slid down the rankings with a series of injury issues, progressed 6-3, 6-2, 6-4 against Alexander Bublik of Kazakhstan.

First round matches are due to continue tomorrow at the US Open.