Roger Federer said he can only get better as the 20-time grand slam champion sent a warning to the rest of the US Open field heading into the third round.

Former world number one and third seed Federer came from a set down for the second match in succession to prevail 3-6 6-2 6-3 6-4 against Damir Dzumhur at Flushing Meadows on Wednesday.

Federer has been far from convincing during the first week in New York, where the five-time US Open champion was uncharacteristically wasteful in his first-round victory over grand slam main draw debutant Sumit Nagal.

Runner-up to Novak Djokovic in a remarkable Wimbledon final before suffering a swift exit from the Western & Southern Open, Federer committed 45 unforced errors against Dzumhur.

Asked about his slow starts at Arthur Ashe Stadium, Federer – who is eyeing his first US Open title since 2008 – told reporters: "I have been in that position many times where you go through a little phase where you don't start so well and everybody asks you right away, 'What are you going to do?'

"You're like, 'I don't know. Just go back to the drawing board. Just do the same things again.' You hope for a better outcome.

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"I don't think there is per se a secret to a good start other than warming up well, being well-prepared mentally, not underestimating your opponent. I did all of that. You know me, I will always do that.

"So when it happens like this in back-to-back matches it's just a bit frustrating more than anything, especially when the level is that low and there is that many errors and the energy is not kind of there. But I can only do better, which is a great thing moving forward."

"I got exactly what I expected from both guys," Federer said when asked if he was surprised in the opening two rounds. "I knew what Nagal was going to give me. I knew what Dzumhur was going to give me. But I didn't expect to hit 15 to 20 unforced errors, which is basically the entire set just sort of donated.

"But look, they came out and they were well prepared and got me to do that. But I clearly have to play better from the get-go."

Federer will meet either Dan Evans or 25th seed Lucas Pouille for a place in the last 16.