Many women have declared they will boycott Twitter on Friday, in solidarity with Rose McGowan, whose account was temporarily suspended.
The actress is among the alleged victims of disgraced film producer Harvey Weinstein and one of the first to speak out.
McGowan has accused Weinstein of rape, but the film producer denies any sexual assaults.
Many of those taking part in the boycott have also shared details of online abuse on the platform.
The hashtag #WomenBoycottTwitter has been shared more than 190,000 times in a matter of hours.
But some social media users have responded to the hashtag with misogynistic abuse and others have questioned whether a boycott is the best way to make the point.
Twitter said Ms McGowan's account had been temporarily locked because one of her tweets violated its terms of service. But many social media users felt she had been silenced.
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A number of high-profile women were among those calling for a boycott, with several highlighting examples of abuse they had suffered online which had not resulted in the suspension of perpetrators' accounts.
Minutes after model Chrissy Teigen tweeted her support for the boycott she shared examples of the abuse she had received online in response, some of it sexually explicit.
Actress Tara Strong also shared examples of abusive and aggressive tweets she had been sent, questioning why Twitter had not taken action.
"They shut down Rose McGowan but not this dude," she tweeted, with images of abusive messages. "Not even joking, his account lives."
Actress Alyssa Milano, who starred alongside Rose McGowan in the TV series Charmed, said that she would be refraining from tweeting for the first time in a decade.
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Many men have also lent their support, including actors Mark Ruffalo and Terry Crews. Crews, a former NFL player who stars in US TV show Brooklyn Nine-Nine, earlier said he had also been the victim of sexual molestation by a Hollywood executive.
"Calling white women allies to recognise conflict of #WomenBoycottTwitter for women of colous who haven't received support on similar issues," she tweeted.