Roger Federer returns the ball to Richard Gasquet during a match in Madrid on Tuesday. Oscar Del Pozo/AFP

Roger Federer shook off a brief bout of pre-match jitters as he returned to clay after a three-year absence, posting a 6-2, 6-3 win over Richard Gasquet on Tuesday at the Madrid Open.

The 20-time Grand Slam champion needed just 52 minutes to brush Gasquet aside in the second round, but confessed he had to control his emotions during afternoon match strategy sessions with his team.

"I was very calm all day, but two hours before, I was feeling it a bit. But that was the only time," Federer said.

"The nerves went away quickly, I'm just happy I started well.

"I'm glad to be back," said the three-time Madrid champion who last played on clay almost three years ago, losing to Dominic Thiem in the Rome third round on May 12, 2016.

Federer skipped the dirt for two full seasons to concentrate on his grass court form, winning Wimbledon in 2017.

He claimed the Madrid title in 2006, 2009, and 2012.

"I've been missing the clay, this is a great return, it's a special night for me," he said.

Federer swept up the opening set in 23 minutes and broke Frenchman Gasquet -- who had defeated him twice on clay -- for 5-3 in the second before serving it out a game later.

Federer has won 18 of 21 meetings with Gasquet, just back from six months out with injury.

Perfect start

Rafael Nadal made the perfect start to his bid for a sixth Madrid Open title on Wednesday by beating Canadian teenager Felix Auger-Aliassime in straight sets.

Nadal has endured a turbulent few weeks after slipping to surprise defeats in both Monte Carlo and Barcelona last month before then being hit by a stomach bug on Sunday.

Rafael Nadal celebrates after beating Felix Auger Aliassime in Madrid on Wednesday. Pierre-Philippe Marcou/AFP

But there was never much sign of an upset in the Spanish capital, where the world number two began with a 6-3, 6-3 victory.

Nadal has not arrived in Madrid without winning in either Monte Carlo or Barcelona since 2015 and, after also pulling out of Indian Wells due to a knee injury in March, concern was growing ahead of the French Open later this month.

The 32-year-old, who will be chasing his 18th Grand Slam title at Roland Garros, will now face another young talent in America's Frances Tiafoe, with either Stan Wawrinka or Kei Nishikori waiting in the quarter-finals.

Djokovic cruises

Novak Djokovic needed just 65 minutes to make a winning start, while Naomi Osaka channelled her inner "zombie mode" to earn a place in the third round.

Top seed and world number one Djokovic hammered American Taylor Fritz 6-4, 6-2 to advance to the last 16 following a premature exit here a year ago.

Novak Djokovic celebrates after winning against Taylor Fritzat in Madrid on Tuesday. Oscar Del Pozo/AFP

"I thought my serve was very efficient today, that's a big advantage," Djokovic said.

"The match was close at the beginning, in the second set I read his serve better and just managed to put an extra ball in to the court.

"It was a solid opening match for me."

Djokovic won the Madrid title in 2011 and 2016. He will be chasing a fourth straight Grand Slam trophy at Roland Garros next month.

Marin Cilic rallied to overcome Germany's Jan-Lennard Struff 4-6, 6-3, 6-4, while 2018 finalist Dominic Thiem advanced when Reilly Opelka quit at 6-7 (2/7), 6-3, 1-0 against the Austrian fifth seed.

Agence France-Presse