However, despite claiming victory, the 34-year-old Swiss admitted he doesn’t know if he will be fit to face Austria’s Dominic Thiem tomorrow after suggesting a back injury that kept him out of last week’s Madrid Open is still troubling him.

Federer, who is seeking a first Rome title having lost last year's final, was on court for the first time since mid-April.

The 17-time Grand Slam champion has played just one event since the Australian Open following knee surgery.

"I was expecting to lose in straight sets today," said Federer, the world number two.

"That was the mind-set going in, so to win in straights is actually a really big surprise to me.

"I played cautious, and I only decided after the warm-up that I was actually going to play.

"I'm happy I was able to play a full match without any setbacks.

"I'm coming off a brutal last few months, and I'm just happy to be able to play normal tennis to some extent.

"So for me, it's a big day and huge step in the right direction."

Thirteenth seed Thiem beat Portugal's Joao Sousa 6-3, 6-2 and must now wait on Federer’s decision over his participation.

Joining them in the third round is defending champion and world number one Novak Djokovic after the Serb defeated French qualifier Stephane Robert 7-5, 7-5.

Spanish fifth seed Rafael Nadal overcame Germany’s Philipp Kohlschreiber 6-3, 6-3, the same scoreline by which British second seed Andy Murray defeated Kazakh qualifier Mikhail Kukushkin in his first match since splitting from coach Amelie Mauresmo earlier this week.

In the women’s draw, three of the top six seeds crashed out with Germany’s Angelique Kerber, Belarus’ Victoria Azarenka and Romania’s Simona Halep all suffering losses. 

Second seed Kerber, the Australian Open champion, was beaten 6-1, 5-7, 7-5 by Canada's Eugenie Bouchard, while fourth seed Azarenka lost 6-3, 6-2 against Romania's Irina-Camelia Begu.

Madrid Open champion Halep, the sixth seed, was beaten 6-3, 4-6, 6-3 by Australia's Daria Gavrilova.