The Serb, 36, prevailed 6-1 6-4 6-4 on Arthur Ashe Stadium to continue his pursuit of a record-equalling 24th Grand Slam title.

Djokovic achieved his victory despite temporarily appearing to struggle with the heat and humidity in New York.

The three-time champion will face home hope Ben Shelton in the last four.

Shelton, in contrast to Djokovic, will be appearing in his first Grand Slam semi-final following his win over compatriot Frances Tiafoe.

Djokovic maintained his perfect record in US Open quarter-finals – with this his 13th win in a row at that stage – to overtake Roger Federer for most Grand Slam men’s semi-final appearances.

The victory also moved him within two wins of equalling Australian Margaret Court’s tally of major singles triumphs.

On achieving another record, Djokovic said: “This is the sport that has given me so much in my life. Coming from Serbia, a war-torn country when I was growing up, I faced a lot of adversity.

“I was lucky to encounter some very knowledgeable and passionate people. Without their support, and my parents, I wouldn’t be here without their love and incredible sacrifice.

“That is the long answer for what goes through my head when I hear those numbers [of records he has broken]. There’s a lot of things I am very grateful for.”

Despite an admirable effort, American Fritz, 25, could not earn any reward as Djokovic delivered a devastating performance in hot temperatures at Flushing Meadows.

The warmest day of the 2023 tournament, with the temperature hitting 32C and high humidity, led to the heat rule being invoked and the roof partially closing to provide shade.

Fritz had a break point in the opening game and showed he would not be overawed by Djokovic when he broke back in game three.

However, Djokovic subdued the growing optimism among the home crowd, efficiently closing out the first set with four successive games.

Despite appearing to struggle with the conditions – the three-time US Open champion crouched down following a couple of points – Djokovic was able to assert himself in set two.

The second seed held firm under pressure, further frustrating Fritz by saving four break points for a 3-1 lead.

Overcoming the physical issues he had faced, Djokovic would not falter and lost just one point in his next three service games.

The third set was by no means straightforward. But, fuelled by the frustration of seeing Fritz immediately break back for 4-4 and angered by the behaviour of an individual in the crowd, Djokovic responded in typical fashion and broke again.

To his credit, Fritz pushed his opponent all the way and reached break point, but Djokovic clinched his second match point after two hours and 35 minutes on court.

The win means Djokovic remains on course for another showdown with top seed Carlos Alcaraz in Sunday’s final, just two months after the 20-year-old edged a thrilling five-set Wimbledon final against the Serb.

Spaniard Alcaraz meets German Alexander Zverev on Wednesday for a place in the last four.