Muchová hit back to 5-4 from 5-1 behind to Gauff in the first set, but a poor service game from the French Open runner-up handed the lead to the home favourite on Arthur Ashe Stadium at the United States Tennis Association Billie Jean King National Tennis Center in New York City.

Gauff held serve in the first game of the second set, but the players were then taken from the arena when three protestors in the stand with tee-shirts demanding "end fossil fuels" began shouting and another glued themselves to the floor.

All four protestors were taken into police custody, and the group Extinction Rebellion claimed responsibility, insisting it was aimed at drawing attention to the "greatest emergency of our time".

The US Open is the latest major sporting event hit by protests against the impact of climate change, with the last tennis Grand Slam Wimbledon in London also targeted.

Play was halted for 49 minutes before resuming, with Gauff converting her sixth match point to triumph 6-4, 7-5.

Afterwards, Gauff admitted she would have preferred the protest not to have taken place during her match, but expressed support for the cause.

"It was done in a peaceful way, so I can't get too mad at it," she said.

"Obviously I don't want it to happen when I'm winning up 6-4, 1-0, and I wanted the momentum to keep going.

"But hey, if that's what they felt they needed to do to get their voices heard, I can't really get upset at it."

The 19-year-old's reached last year's French Open final where she lost to Iga Świątek of Poland, and her previous best run at the US Open came last year to the quarter-finals.

Soon-to-be world number one Aryna Sabalenka, a Belarusian player competing as a neutral due to the war in Ukraine, denied an all-American final with a stirring comeback victory against Madison Keys.

Sabalenka is already the first player since American great Serena Williams in 2016 to reach the semi-finals of all four Grand Slams in a calendar year, but the Australian Open winner found herself on the brink of defeat to world number 17 Keys, attempting to reach her second US Open final after a 2017 defeat to compatriot Sloane Stephens.

Keys stormed to the first set 6-0, and Sabalenka was handed a code violation having lost serve to trail 2-1 in the second.

At 5-4 in front, Keys was serving for the match, but Sabalenka hit back and although she failed to convert two set points at 6-5 ahead, she prevailed 7-1 in a tiebreak to level the match.

Keys was first to break again in the final set to lead 4-2, but Sabalenka forced another tiebreaker and held her nerve to prevail 10-5 in an epic that lasted two hours and 35 minutes.

It was a sweet moment for Sabalenka, who had lost in three sets at the US Open semi-finals for the last two years.

In the men's doubles semi-finals on Louis Armstrong Stadium, India's Rohan Bopanna playing with Australia's Matthew Ebden sealed a return to the US Open final 13 years on from his last, beating former champions Pierre-Hugues Herbert and Nicolas Mahut of France 7-6, 6-2.

Their opponents are set to be Rajeev Ram of the US and Britain's Joe Salisbury, who overcame second seeds Ivan Dodig of Croatia and Austin Krajicek of the US 7-5, 3-6, 6-3.

Men's singles semi-finals are set to be held tomorrow at the US Open, with Gauff facing Sabalenka in the women's singles decider on Saturday (September 9).