Yvette Cooper has said that she has informed police and Twitter about a tweet in which a user threatened to kill her children and grandchildren.

The Labour MP, who has been campaigning for a remain vote in this week’s EU referendum, posted an image on Tuesday of the tweet, which was sent from an account which had been suspended on Tuesday night and accused her of issuing propaganda.

“Got this today for speaking out for Remain … This has to stop,” said Cooper, a former minister who represents the West Yorkshire constituency of Normanton, Pontefract and Castleford.

Got this today for speaking out for Remain..... This has to stop. pic.twitter.com/HPV8asrZ3w — Yvette Cooper (@YvetteCooperMP) June 21, 2016

Cooper said in a later tweet that the police and Twitter were “on the case” after she had lodged a report.

“But this is for all of us. Time to stop the hatred,” she said.

The incident comes after MPs’ security has been increased following the killing of Cooper’s colleague, Jo Cox, who also represented a West Yorkshire constituency.

The National Police Chiefs’ Council (NPCC) said the advice was to help politicians to take appropriate measures to deal with any risks or threats they faced.

Cooper joined other MPs earlier this year to launch an online public consultation as part of a national campaign against abuse aimed at women on social media.

Using an online forum, she has been calling for contributions from individuals, organisations, employers, union members, victims, police and tech companies.

The campaign comes after research for the Guardian’s project the web we want revealed that of the 10 most abused writers online, eight were women and the other two were black men.