World number one Jannik Sinner and four-time Grand Slam champion Carlos Alcaraz were both given scares in their US Open first-round matches.

Italy's Sinner lost the first set before regrouping to beat American Mackenzie McDonald 2-6 6-2 6-1 6-2 on the second day's play in New York.

The Italian was playing his first match since it emerged he had been cleared of any wrongdoing after twice testing positive for a banned substance earlier this year.

Alcaraz, the reigning French Open and Wimbledon champion, overcame a scrappy second set to see off Australian qualifier Li Tu 6-2 4-6 6-3 6-1.

The pair, whose rivalry is tipped to be one to watch over the next few years, could meet in the semi-finals at Flushing Meadows.

Earlier on Tuesday, Stefanos Tsitsipas suffered an early US Open exit for the seventh year in a row as the 11th seed lost to Thanasi Kokkinakis in the first round.

But last year's runner-up and 2021 champion Daniil Medvedev brushed off a middling second set to beat Dusan Lajovic for his 30th match win in New York.

Sinner, whose coach said he was "physically and mentally" worn down by the investigation, found himself a set and a break down after a poor start on Arthur Ashe Stadium.

But he found his footing midway through the second set and it was plain sailing from there for the 23-year-old.

Sinner said the overall response to news that he had tested positive twice for a banned substance was "not bad".

"The response from fans, I feel it has been great - throughout when the news came out, in the practice sessions, there was a lot of support, which I'm very glad and happy about that," Sinner said in a news conference.

Asked about the reaction from other players he said: "I cannot control the players' reaction, and if I have something to say to someone, I go there privately, because I'm this kind of person."

Alcaraz, by contrast, started strongly, quickly finding himself a set and a break up before the unforced errors started to creep up.

However, he readjusted well in the third set and was dominant in the fourth, finishing with 50 winners to his opponent's 19.

Alcaraz is bidding to become the third man in history after Rod Laver and Rafael Nadal to win the French Open, Wimbledon and the US Open in the same calendar year.

When asked about the statistic on ESPN, he joked: "Well, after this interview I’m going to try to pretend I never heard that.

"Obviously it would be a great achievement if I make it, but it is going to be difficult."

He and Sinner are the favourites to challenge defending champion Novak Djokovic, who beat Alcaraz just three weeks ago to clinch Olympic gold.

Greek Tsitsipas has never gone beyond the third round in New York, losing in the first round on three occasions.

He struggled for consistency once again in a 7-6 (7-5) 4-6 6-3 7-5 loss to Australian world number 86 Kokkinakis.

Tsitsipas is the highest-ranked player to lose on the men's side of the draw in the first two days at Flushing Meadows.

A two-time Grand Slam finalist, Tsitsipas has had a mixed year, with his best major showing a quarter-final appearance at the French Open.

He halted his coaching partnership with his father in the lead-up to the US Open, having being critical of his coaching tactics in his recent Cincinnati Open exit.

But Tsitsipas had his chances against Kokkinakis - he was 40-0 up on serve at 3-4 down in the third set before being broken and was broken cheaply at 5-5 in the fourth.

Tsitsipas converted just three of his 10 break point opportunities, compared to four out of eight by Kokkinakis in the near four-hour match.

Canadian 19th seed Felix Auger-Aliassime also suffered a first-round exit, after he was thrashed 6-2 6-4 6-2 by Czech teenager Jakub Mensik.

But seventh seed Hubert Hurkacz, continuing his return from knee surgery, beat Kazakh Timofey Skatov 6-3 7-6 (7-4) 7-6 (7-3).

Swiss veteran Stan Wawrinka, 39, was knocked out in a 6-4 7-6 (7-5) 6-3 defeat by Italy's Mattia Bellucci, while 10th seed Alex de Minaur needed four sets to move past Marcos Giron.