Novak Djokovic began his bid for a calendar Grand Slam by eventually easing through against injured Danish qualifier Holger Rune at the US Open.

German fourth seed Alexander Zverev started his bid with a straight-set victory against American Sam Querrey.

The 24-year-old – who reached the final in 2020 – wrapped up his routine 6-4 7-5 6-2 win in one hour and 40 minutes.

Zverev is looking to add a first Grand Slam title to the Olympic gold he won in Tokyo at the start of August.

Djokovic’s bid to become the first man to win a ‘Golden Slam’ – all four Grand Slams and the Olympic title in the same year – was ended by Zverev in the Tokyo 2020 semi-finals.

But the world number one is still the heavy favourite to win at Flushing Meadows and become only the sixth player to complete a clean sweep of the Australian Open, French Open, Wimbledon and US Open.

Additionally, it would be the Serb’s 21st major title – an outright men’s record. It would move him clear of Roger Federer and Rafael Nadal for the first time.

Questions for Djokovic after uncertain start

Djokovic, 34, was tuned in during an impressive start against former junior world number one Rune, serving strongly and not missing a return on his opponent’s first serve in a 26-minute opening set.

But his focus drifted in the second. Rune broke for a 3-0 lead as Djokovic started to hesitate, the Serb fighting back to lead 4-3 before hitting a double fault to put the set back on serve.

Boosted by the backing of a buoyant crowd on Arthur Ashe Stadium, the Danish teenager impressively won the second-set tie-break and lapped up the acclaim.

A sloppy service game from Rune enabled Djokovic to break for a 3-1 lead in the third set, before the youngster became impeded by cramp in his left leg.

Unable to walk properly between points and shaking his head in frustration, the world number 145 continued to play despite regularly receiving treatment.

The match was long over as a contest and could not provide a true gauge of Djokovic’s form as the Serb eased through the fourth set to tee up a meeting with Tallon Griekspoor of the Netherlands.

“It’s never nice to finish the match the way we finished today. Holger is an up and coming star and it is unfortunate he had to go through that,” said Djokovic, who consoled Rune at the net.

“It wasn’t the best of my performances but he played well in the second set when it mattered. I stayed in the moment and rectified the errors I had.

“After that it is difficult to talk much about the match. He couldn’t move much.”

Zverev leads the challenge of the ‘young guys’, with wins for Shapovalov & Berrettini

Zverev is one of the in-form players on the ATP Tour after backing up his Olympic triumph with victory at the Cincinnati Masters.

The 2021 French Open semi-finalist took advantage of two error-strewn games from world number 78 Querrey, 33, for late breaks in the first two sets and pulled away in the third for a dominant win.

He will face Albert Ramos-Vinolas in the next round after the Spaniard came through in five sets against France’s Lucas Pouille.

Zverev, who could face Djokovic in the semi-finals, said after his win: “Novak is chasing history but I think the young guys are going to try and get in the way of that and I am looking forward to maybe giving him a challenge as well.”

Canadian seventh seed Denis Shapovalov stormed into the second round with a 6-2 6-2 6-3 victory over Federico Delbonis, taking one hour and 49 minutes to see off the Argentine.

Sixth seed Matteo Berrettini also made it through in straight sets, with the Italian needing two tie-breaks to overcome Frenchman Jeremy Chardy 7-6 (7-5) 7-6 (9-7) 6-3.

But ninth seed Pablo Carreno Busta went down to American qualifier Maxime Cressy, who served 44 aces to come from two sets down to win 5-7 4-6 6-1 6-4 7-6 (9-7).

Japan’s Kei Nishikori, runner-up in 2014, beat Italy’s Salvatore Caruso 6-1 6-1 5-7 6-3 and will face Mackenzie McDonald after the American knocked out Belgian 27th seed David Goffin in straight sets.

Russian 25th seed Karen Khachanov also suffered a surprise first-round exit at the hands of South Africa’s Lloyd Harris, going down 6-4 1-6 4-6 6-3 6-2 to the 24-year-old world number 46.

Meanwhile, American prospect Sebastian Korda lost the first set of his meeting with Georgia’s Nikoloz Basilashvili 6-2 and was 2-1 down in the second before he retired. It was not clear why he could not continue but the 21-year-old withdrew from the Toronto Masters with a back injury earlier this month.

There were also wins for Polish 10th seed Hubert Hurkacz, Italian 13th seed Jannik Sinner and France’s Gael Monfils, the 17th seed.