Novak Djokovic called on US Open organisers to find a solution to the humidity problems on Arthur Ashe Stadium after sweating his way through to the semi-finals.

The Wimbledon champion has struggled in the unusually extreme conditions in New York this year and was again in discomfort during a 6-3, 6-4, 6-4 victory over Australian John Millman that lasted nearly three hours.

Both Roger Federer and John Isner suggested the roof structure added to Ashe two years ago has made conditions more stifling, with Federer complaining of not being able to get any air during his shock defeat by Millman.

Djokovic, for whom this was an 11th consecutive quarter-final victory, said: “I personally have never sweated as much as I have here. I have to take at least 10 shirts for every match. It’s literally after two games you’re soaking. And Roger, he never sweats that much. But we saw him a couple of nights ago.

“I asked the chair umpire whether they are using some form of ventilation or air conditioning down at the court-level side, and then he says that he’s not aware of it, only what comes through the hallways.

“I think that this tournament needs to address this. Because whether it’s night or day, we just don’t have air down there. It feels like a sauna. This has been definitely the toughest US Open in the last 10 years that I have played in in terms of conditions.”

Djokovic refused to reveal what the tablets were that he was demanding from his team during the match, while he was also given a nasal spray from the doctor.

That came during an unusual stoppage after four games of the second set when Millman was instructed to go off court to change his whole kit because he was sweating so much it was making the surface dangerous.

Djokovic, grateful for a bit of a breather, sat grinning in his chair with his shirt off, much to the crowd’s amusement.

Millman said: “It was a tricky one coming off. I didn’t really want to come off. I felt like I had a good bit of momentum there. But that’s tennis. That’s fine.

“These night matches, the humidity goes through the roof. You’re dripping. But that’s no excuse or anything. I’d play in a swimming pool if I got to play a quarter-final every week at a Grand Slam.”

Djokovic threatened to pull away all through the match, but was never able to shake off Millman.

The Serbian won only four of 20 break points against an opponent whose surprise run has been one of the stories of the tournament.

Djokovic, who next faces Kei Nishikori in a repeat of the 2014 semi-final which he lost, said: “I was, I think alongside many other people, anticipating the match against Federer, and it was a surprise to see Millman win the match.

“I watched the second part of the match and Roger was not playing well. He was missing a lot. But Millman is the kind of player that makes you miss and makes you earn the point.

“I really have respect for him. He’s a great fighter. Just an all-around player. I think he has had probably the tournament of his life and a match of his life against Roger. He made me run and he made me earn my match today.”