The former world number one, three-time major winner and back-to-back Olympic champion came back from two sets and a break down to beat Japan’s Yoshihito Nishioka in an almost five hours on Tuesday (September 1), but was powerless to stop the 20-year-old Canadian who triumphed 6-2, 6-3,6-4 in New York.

The 33-year-old, who underwent a career-saving hip resurfacing operation in January 2019, admits it will be "extremely difficult" to add to his Grand Slam collection, but is refusing to give up on achieving that feat.

"I would say I’m more positive about what I could do in Grand Slams than I was before I came over here," Murray said after the defeat.

"I mean, you know, you guys obviously don’t know how I was feeling even just a couple of months ago.

"So like I said, to come over here and play, you know, I played a couple of tough matches in Cincinnati and I played certainly one very tough match here, and my right hip felt good.

"That’s really, really positive."

"‘There is other things, like I said, that need to get better, but I would say that I’m more positive now than what I was a couple of months ago, that’s for sure.

"In terms of winning Grand Slams again, that’s going to be extremely difficult to do.

"It was hard enough when I had two normal hips, so it will be difficult, but I’ll keep trying, like, why not?"

Auger-Aliassime is now set to meet either Britain’s Dan Evans or Frenchman Corentin Moutet, who was leading 4-6, 6-3, 6-5 before rain forced the second-round encounter on Court Five to be suspended.

Elsewhere, Vasek Pospisil downed fellow Canadian Milos Raonic 6-7 (1-7), 6-3, 7-6 (7-4), 6-3, while Hungary’s Márton Fucsovics knocked out Bulgarian number 14 seed Grigor Dimitrov 6-7 (5-7), 7-6 (7-4), 3-6, 6-4, 6-1 in a thrilling match.

American Frances Tiafoe also prevailed in five sets, defeating Australia’s John Millman 7-6 (8-6), 3-6, 1-6, 6-3, 6-3 to advance to the US Open third round for the first time in his career.

Last year’s runner-up, Daniil Medvedev of Russia, defeated Christopher O’Connell 6-3, 6-2, 6-4 in the Louis Armstrong Stadium.

Prior to that match, Sloane Stephens swept aside Belarusian Olga Govortsova 6-2, 6-2, setting up a mouth-watering all-United States tie against Serena Williams.

Williams continued her quest for a record-equalling 24th Grand Slam singles title with a 6-2, 6-2 victory over Russian Margarita Gasparyan on the Arthur Ashe Stadium.

But the 38-year-old, who has yet to win a major since the Australian Open in 2017, says she is trying not to heap too much pressure on herself.

"The only thing that gets me flustered is really me, like, because I always feel like I'm not winning every point," Williams said, as reported by Yahoo.

"I have been going back and looking at me and that's not what I normally do.

"Usually I'm just calm.

"And I just think with the pressure and everything that I felt, I felt like I just needed to be perfect.

"I always feel like I'm not perfect unless I'm perfect. That's not a fun way to live your career and live your life."

 In the other night match, Victoria Azarenka ousted number five seed and fellow Belarusian Aryna Sabalenka 6-1, 6-3.