US Open winner Dominic Thiem swept into the last 16 at Roland Garros on Friday along with women's third seed Elina Svitolina while Rafael Nadal anticipated a stiffer challenge after serene progress in his first two matches at the tournament.

Former champion Simona Halep faces a fascinating rematch with Amanda Anisimova, the American teenager who knocked her out of last year's competition.

Thiem broke down early resistance from Norway's Casper Ruud to secure an impressive 6-4, 6-3, 6-1 victory and set up a possible showdown with 2015 French Open winner Stan Wawrinka.

"I'm very happy. It was a great match and I didn't do any mistakes," said Thiem, the runner-up to Nadal the past two years. "The conditions are very nice to play in under the roof - no wind and the court is perfect."

Wawrinka, the 16th seed, goes up against the lone Frenchman remaining in the draw, Hugo Gaston, the world number 239. Two-time quarter-finalist Svitolina ensured she will stick around for the second week in Paris with a 6-4, 7-5 win over Russia's Ekaterina Alexandrova, the 27th seed.

Ukrainian Svitolina is full of confidence after capturing her 15th career WTA at Strasbourg last weekend. "It's always really nice to have another chance to go deep in the tournament," said Svitolina. "It's a little bit different without the crowd, so you start to treasure every match and every Grand Slam you play."

Polish teenager Iga Swiatek dismissed former Wimbledon finalist Eugenie Bouchard 6-3, 6-2 to seal a return to the last 16, matching her best result at a Grand Slam. Later on Wednesday, 12-time champion Nadal meets 74th-ranked Italian Stefano Travaglia, who is through to the last 32 of a Grand Slam for the first time.

Unsurprisingly, Nadal has yet to drop a set in Paris against opponents with a combined ranking of 319, but the Spaniard knows tougher examinations await in his pursuit of Roger Federer's record 20 major titles.

"I've won two matches in three sets. When you win like this it's not bad, it means you don't make many mistakes and manage to make a difference," said Nadal. "It's a good thing. I know in the next round more is going to be asked of me and I need to be ready for that."

Painful memory spurs on Halep

Halep's status as the women's favourite was reinforced following the withdrawal of Serena Williams, on top of the absence of world number one and defending champion Ashleigh Barty, as well as US Open winner Naomi Osaka.

The Romanian is riding a career-best 16-match winning streak but is well aware of the threat posed by her upcoming opponent. Anisimova, who turned 19 in August, became the first player born in the 2000s to reach the last four at a major when she defeated Halep in the quarter-finals last year.

"I'm going to talk with the coach, I know it's going to be tough because she's hitting the ball strong and flat, so it's going to be tough," said Halep. "I remember the match from last year, I remember also that I didn't play what I wanted, so I will do some changes and I will just try to play better and to take my chance."

Sixth seed Alexander Zverev tackles Italian qualifier Marco Cecchinato, who famously beat Novak Djokovic on his way to a semi-final appearance at Roland Garros in 2018. Zverev was again taken to five sets in round two -- 31 percent of his Grand Slam matches have now gone the distance, compared to just nine percent for Nadal.

Kiki Bertens will attempt to move on her from her stormy win over Sara Errani after which the Dutch fifth seed departed the court in a wheelchair.

Former finalist Errani accused Bertens of faking injury during a three-hour clash which left her in cramps and the Italian screaming an obscenity.