Osaka was due to face Olga Danilovic of Serbia however the 20-year-old, ranked number 145 in the world, pulled out of the contest.

The women’s seeds that were in action enjoyed a good day with routine wins, including second seed Aryna Sabalenka of Belarus who defeated Slovenia’s Tamara Zidansek 6-3, 6-1.

Sabalenka’s victory came despite her commenting afterwards that she was "scared" she had broken her hand during a fall in the first set.

Fifth seed Elina Svitolina of Ukraine also progressed in straight sets defeating Spain’s Rebeka Masarova 6-2, 7-5.

Eighth seed Barbora Krejcikova of the Czech Republic defeated Christina McHale of the United States 6-3, 6-1 in a contest completed on the Louis Armstrong Stadium Court under the roof after rain forced a delay to play on the outside courts.

Ninth seed Garbine Muguruza of Spain overcame Andrea Petkovic of Germany 6-4, 6-2, while 12^th seed Simona Halep of Romania, whose match was moved on to the Arthur Ashe Stadium with Osaka receiving a bye, defeated Kristina Kucova of Slovakia 6-3, 6-1.

Halep is tied with Kazakhstan’s 19^th seed Elena Rybakina in the next round after she beat France’s Caroline Garcia 6-1, 6-4.

Other women’s seeds to win their second round matches in the day session on day three at Flushing Meadows included last year’s runner-up Victoria Azarenka of Belarus, who overcame Jasmine Paolini of Italy 6-3, 7-6, and 20^th seed Ons Jabeur of Tunisia, who dropped just one game in beating Maria Osorio Serrano of Colombia 6-0, 6-1.

America’s 2017 US Open champion Sloane Stephens also reached the third round with a 6-4, 6-2 victory against her compatriot and the 21^st seed Coco Gauff.

The second round match between former US Open winner and 16^th seed Angelique Kerber of Germany and Ukraine’s Anhelina Kalinina is the only one in the bottom half to be completed, while in the top half of the draw, world number one Ash Barty of Australia faces Dane Clara Tauson and Canada’s 2019 US Open champion Bianca Andreescu plays American Lauren Davis.