Newspaper reports at the weekend quoted backbenchers as saying the prime minister would be “knifed” and telling her to “bring her own noose” to a meeting of MPs.
MPs from across the political spectrum have lined up to condemn the graphic comments.
Many said parliamentarians should remember the 2016 murder of Labour’s Jo Cox, who was fatally shot and stabbed by a neo-Nazi terrorist.
Former Brexit minister Steve Baker said in the Commons that disciplinary action should be taken.
He added: “The person or persons who directed violent language at (Mrs May) have thoroughly disgraced themselves.
“I very much hope that they are discovered and I hope that she will withdraw the whip from them.”
The PM thanked her Conservative colleague for the “supportive comments he’s made about the language that was used at the weekend”.
Labour leader Jeremy Corbyn also criticised the rhetoric, saying he hoped the debate following Mrs May’s statement on Monday would be conducted “without some of the language reported in the press over the weekend”.
Mrs May replied: “I think it is incumbent on all of us in public life to be careful about the language we use, there are passionate beliefs and passionate views that are held on this subject and other subjects but whatever the subject is we should all be careful about our language.”
Labour’s Yvette Cooper, chair of the Home Affairs Select Committee, hit out at the “violent, dehumanising and frankly misogynistic language”.
Tory MP Amber Rudd, a former home secretary, said she hoped she would not see “any sort of language like that in the future”.
Earlier, Mrs May’s official spokesman said the PM expected public figures to avoid “dehumanising” and “derogatory” language.
“I don’t intend to dignify those specific anonymous comments with a response,” the spokesman told journalists at a regular briefing.
“The prime minister has always been very clear that we must set a tone in public discourse that is neither dehumanising nor derogatory.
“Personal vitriol has no place in our politics.”