Aryna Sabalenka kept her cool to win a politically-charged French Open duel against Marta Kostyuk on Sunday as jeers rained down after the defeated Ukrainian refused to shake hands with her Belarusian opponent.

World number two and Australian Open champion Sabalenka swept 10 of the last 12 games to win 6-3, 6-2 as she kick-started her push to reach the second week in Paris for the first time.

Kostyuk honoured her pledge not to shake hands with Sabalenka in protest at Russia's war in Ukraine. Belarus is a key military ally of Moscow.

"It was a very tough match, tough emotionally. I didn't know if the booing was against me but thank you so much for your support, it's really important," said Sabalenka who performed a theatrical bow to the sparse Court Philippe Chatrier crowd.

Kostyuk, 20, famously refused to shake hands with Sabalenka's Belarusian compatriot and former world number one Victoria Azarenka at the US Open last year.

She opted instead for a cursory touch of racquets at the net.

The 39th-ranked Kostyuk has been a vociferous critic of the decision to allow Russian and Belarusian players to keep competing on tour since the assault on her country. (AFP)