The Prime Minister was told to “step aside” by Conservative MP Andrea Jenkyns during a heated Commons debate.
The comment came during Prime Minister's Questions, with Ms Jenkyns accusing Mrs May of failing "to deliver on her promises".
"She has tried her best and nobody could fault or doubt her commitment and sense of duty, but she has failed," Ms Jenkyns said.
“She has failed to deliver on her promises and we have lost 1,300 hard-working councillors.
“Sadly the public no longer trusts her to run the Brexit negotiations. Isn’t it time to step aside and let someone new lead our party, our country and the negotiations?”.
Theresa May dismissed the criticism saying that Conservative losses in the recent local elections were not related to her leadership of the party.
“I have been a councillor, I know the hard work and dedication that it takes,” she said. “I have also been a councillor who has stood in an election against a difficult national background under a Conservative government – I know what that feels back.”
She added: “This is not an issue about me and it is not an issue about her. If it were an issue about me, and how I vote, we would have already left the European Union.”