An MP who received rape threats on Twitter called in the police on Monday amid growing pressure on the social networking site to tackle abuse.

The Association of Chief Police Officers (Acpo) joined calls on Monday for the site to improve the way it deals with internet trolls, as more than 60,000 people signed a petition demanding the social network improve its regulation of abusive users.

Stella Creasy MP was targeted after defending the campaigner Caroline Criado-Perez, who was threatened with rape and murder on Twitter after successfully lobbying for women to be commemorated on banknotes.

Download the new Independent Premium app Sharing the full story, not just the headlines

Ms Creasy reported a stream of violent threats she received on the site and pledged to take on abusers. One message sent to the Labour MP yesterday said: “You better watch your back... Im [sic] gonna rape your ass at 8pm and put the video all over the internet.”

Another sent late on Sunday night from a Twitter account called @rapey1 threatened: “i will rape you tomorrow at 9pm .... shall we meet near your house??????”

Creasy re-tweeted the messages on her own page using the slogan #takebacktwitter and reported the user to the police. Commenting on her experience, she said “This is not about Twitter, this is about hatred of women and hatred of women who speak up. And indeed, some of those people sending the messages have been absolutely explicit about that.”

She added: “Twitter needs to be explicit that sexual violence and sexual aggression will not be tolerated as part of their user terms and conditions. We can all challenge these people and when this happens to me in other occasions I tend to retweet it so people can say, ‘This is not acceptable’.”

The classicist Mary Beard was also subject to “highly offensive” sexually explicit abuse on the site yesterday and managed to stop it after naming and shaming the man. Professor Beard, who is professor of classics at the University of Cambridge, retweeted a post from Oliver Rawlings which read: “retweet this you filthy old slut. I bet your vagina is disgusting.”

Other users responded by condemning Mr Rawlings – and even threatening to send Professor Beard his mother’s address, so she could report him. Within minutes he responded: “I sincerely apologise for my trolling. I was wrong and very rude. Hope this can be forgotten and forgiven.”

The chairman of Acpo communications advisory group, Andy Trotter, said that Twitter was not doing enough to combat internet trolls. “I think there is a lot more to be done”, he said.

“They need to take responsibility as do the other platforms to deal with this at source and make sure these things do not carry on. They need to make it easier for victims to report these matters and, from a police perspective, they need to know that they can report these things to us.”

In an interview on BBC Radio 4, Mr Trotter said officers did not want to be “policing the internet all day long”, but “when it comes to really outrageous behaviour, it must be reported to us and we will deal with these people.”

A Change.org petition set up in the wake of the Criado Perez abuse at the weekend now has 62,000 signatures. It is calling for the site to have a “zero-tolerance” position on abuse and introduce a “report abuse” button.

A Twitter spokeswoman said: “The ability to report individual tweets for abuse is currently available on Twitter for iPhone, and we plan to bring this functionality to other platforms, including Android and the web. She added: “We don’t comment on individual accounts. However, we have rules which people agree to abide by when they sign up to Twitter. We will suspend accounts that, once reported to us, are found to be in breach of our rules.”