Fernández, who is contesting a Grand Slam as the top-ranked player for the first time in his career having assumed the status in July, registered a 1-6, 6-1, 7-5 win over Peifer at Flushing Meadows in New York City.

"It’s a lot of pressure, but it’s a good pressure, and I’m trying to start to get used to it," Fernández, a winner of seven titles this season, said.

"It’s different being number one going to a tournament, but I’ve been doing well so far."

Awaiting Fernández in the semi-finals is another Frenchman, Stéphane Houdet, who beat Sweden’s Stefan Olsson 6-3, 6-3.

"You know, in the past when we made the draw you used to think, 'I’d love to play this guy or this guy'," Houdet, the 2013 US Open champion, said.

"Not anymore.

"You can pick anyone and you can win or lose, so the draw is useless."

In the other half of the draw, Gordon Reid and Alfie Hewett both won their quarter-final encounters to set up the first all-British Grand Slam singles semi-final.

World number two Reid defeat Belgium’s Joachim Gerard 6-7, 6-4, 6-1 in his opening match to reach the penultimate round for the second time since 2013.

World number three Hewett, meanwhile, came from a set and 3-1 down to overcome six-time US Open champion Shingo Kunieda of Japan 4-6, 6-4, 6-3.

The only non-Dutch semi-finalist in the women’s singles event is world number one Yui Kamiji after the Japanese opened her bid for a second US Open title by beating Great Britain’s Lucy Shuker 6-1, 6-0.

Next up for Kamiji is 2013 champion Aniek van Koot, who defeated South Africa's Kgothatso Montjane 6-4, 6-2.

Also through to the semi-finals is Diede de Groot thanks to a 6-2, 6-4 triumph over Germany’s Sabine Ellerbrock in a repeat of the outcome of the Wimbledon final in July.

De Groot meets fellow Dutchwoman Marjolein Buis for a place in the final after she ended the challenge of American wildcard Dana Mathewson with a 6-2, 6-3 win.

In the quad singles, world number one David Wagner remains unbeaten after overcoming world number two Andy Lapthorne of Britain 6-2, 6-4.

It follows a victory over fellow American and US Open first-timer Bryan Barten yesterday.

Lapthorne goes into the last set of round-robin matches tomorrow with the same one win and one loss record as Australia’s Dylan Alcott, upon whom he inflicted a first defeat since January 2016 yesterday.

Alcott, the 2015 champion, bounced back today to beat Barten 6-2, 7-5.

Yesterday saw the men’s and women’s doubles finalists decided as wheelchair tennis was contested on Arthur Ashe Stadium for the first time.

Second-seeded men’s doubles pairing Hewett and Reid posted a 6-3, 6-2 win over Fernández and Kunieda in the inaugural wheelchair match on the main court of the US Open.

They will play top seeds Houdet and Peifer in the final after they defeated Gerard and Olsson 6-3, 5-7 (10-8).

In the first of the women’s doubles semi-finals, the unseeded duo of Mathewson and Van Koot upset second seeds Kamiji and Shuker 0-6, 6-4 (10-5).

Their fellow finalists are Rio 2016 Paralympic silver medallists Buis and De Groot after the Dutch top seeds recorded a 6-3, 6-2 win over Ellerbrock and Montjane.