Russian star Daniil Medvedev believes he still has a distance to go before he can be considered a genuine Grand Slam contender after sprinting into the second round of the US Open.

Fifth seed Medvedev required just 85 minutes to dispatch India’s Prajnesh Gunneswaran 6-4, 6-1, 6-2 on Monday and book a meeting with Bolivian outsider Hugo Dellien.

“I can’t say I’m feeling amazing about my game but to win by that score in the first round is great,” Medvedev said. “I hope I can continue to play well.”

Medvedev cracked the top five for the first time following his triumph at this month’s Cincinnati Masters, where he defeated Novak Djokovic en route to the title, improving on runner-up finishes at Montreal and Washington in the preceding weeks.

Tipped as a potential candidate to end the dominant run of Djokovic, Rafael Nadal and Roger Federer at Grand Slams, Medvedev, who has yet to go beyond the last 16 at a major, was quick to cool expectations.

“I always try to stay at the same time a little bit away (from this talk), because I always say at this moment of my career I haven’t even been in the quarters of a Slam yet,” he said.

“So that’s the first step to make, and if I make this step, then I can talk about bigger goals and bigger achievements.”

The 23-year-old Medvedev leads the ATP Tour with 45 wins this season and his six finals appearances are the most of any player.

“I think talking about my confidence inside of me, I would say I was already confident in the other Grand Slams,” said Medvedev.

“But talking about my confidence in my tennis game, of course, it grew a lot just because, I mean, these last three weeks they were, without a doubt, the best in my career.

“Because even this year I still had my ups and downs in some tournaments, and these three weeks I basically didn’t have any downs. I had only great matches.”

Medvedev particularly impressed during a semi-final win over Djokovic in Cincinnati, turning up the aggression mid-match to knock off the defending champion in three sets.

“It gives a lot of confidence to me that I’m able, as you said with Novak, for example, to change my game and the momentum and start to give him problems,” said the Russian.

“Hopefully I can bring this confidence on the court, and as you say, hopefully for two weeks or more.”