Roger Federer is "feeling better every day" after returning to the court with a straight-sets win over Peter Gojowczyk at the Cincinnati Masters on Tuesday.

Federer had not played since losing his Wimbledon quarter-final to Kevin Anderson last month but showed no signs of rust as he cruised to a 6-4 6-4 victory.

Leonardo Mayer awaits in the third round and Federer feels confident about the hard-court season.

"I felt good in that first match, to be honest, walking out, hardly any nerves," Federer said. "I think I knew what I wanted to do, what I had to do. The game plan is very simple. It's straightforward, it's fast-court tennis."

"I'm only feeling better every day that has gone by after Wimbledon. It's nice to have played a match so my last match is not the Anderson match. So you've kind of turned the page, I guess, in that regard. It's a good thing."

"I do believe usually it takes two or three matches to get going... like aiming for the lines, finding the rhythm on the serve, being able to serve very accurately time and time again, getting used to the balls, how the ball flies."

"That's why I'm always happy when I clear the first hurdle of any event, because it gives me an opportunity to actually play better the next time around."