A chess commentator has been sacked for making sexist remarks during the coverage of a top women's tournament. 

During a live broadcast of the FIDE Women's Grand Prix event in Kazakhstan, the Belarusian-born Israeli grandmaster Ilya Smirin admitted to saying chess is "maybe not for women".

"I didn't say it openly," he told his co-commentator, Women's International Master Fiona Steil-Antoni.

"It was a private conversation."

Steil-Antoni responded by reminding him of an earlier remark in which he'd praised a woman for "playing like a man".

"Yeah, it's true," Smirin said.

"She's playing in style — positional style. A very strong endgame."

Smirin's comments provoked criticism from several top female players.

"Shockingly unacceptable!" said former Women's World Champion Susan Polgar.

"Swift action must be taken before the next game."

Two-time US Women's Champion Jennifer Shahade said it was "gross to see such sexism in the broadcast for a women's event".

The International Chess Federation (FIDE) issued a statement on Wednesday night (AEST), describing the comments as "very embarrassing". 

"Although we have great respect for Grandmaster Ilya Smirin as a chess player, the views he expressed on air are completely unacceptable, offensive, and do not represent any of the values that FIDE stands for," it said.

"Therefore we unreservedly apologise to all those who were offended."

FIDE said Smirin had been stood down from his commentary duties with immediate effect.

"FIDE not only strives to increase women's representation in professional sports and official positions but also to change the perception of chess as purely a men's world," it said.

"Our community has to be a place where women feel safe and respected."