World number two Aryna Sabalenka of Belarus powered past Ukraine's Elina Svitolina 6-4 6-4 in a highly anticipated clash on Tuesday to reach the French Open semi-finals.

The match was an intriguing prospect with Svitolina, who last year became a mother, refusing to shake hands with players from Russia or Belarus following Moscow's invasion of Ukraine last year, which it calls a 'special military operation'.

Australian Open champion Sabalenka, who next faces Czech Karolina Muchova, caused a furore by snubbing the media after her last two matches, havingbeen grilled about the war and her country's involvement as a staging ground for Russian troops.

But she was all business on Court Philippe Chatrier, cruising through her quarter-final in straight sets despite a flurry of 37 unforced errors compared to her opponent's 12.

"She's a tough opponent, she moves very well," Sabalenka said of her challenging start to the game. "What she did after giving birth is impressive I have respect for her.

"I'm happy with the win and the atmosphere," the Belarusian added. "We all know you are waiting for Novak (Djokovic who plays next) but I'll take it as if it's for me."

With several Ukrainian flags unfurled in the half-empty stands, the pair traded blows at the start with neither managing to carve out a break point in the first eight games.

But favourite Sabalenka, aiming for the world number one spot with a title win in Paris, grabbed the key break and then served out the first set a little later, with her opponent looping a backhand wide.

Svitolina broke for 2-0 in the second set as Sabalenka hit her 23rd unforced error but the Ukrainian was still on the back foot in most points and allowed her opponent to pull the break back when she netted a backhand.

Sabalenka continued her demolition job, breaking again for 3-2 with a forehand winner.

Svitolina stayed afloat thanks to her opponent's unforced errors, but the outcome was always in the Belarusian's hands.

Sabalenka ended it on the second match point with yet another forehand winner and boos were heard from the stands as Svitolina walked straight to her bench without shaking hands, while Sabalenka waited at the net.