After being issued with a demand to set out a clear timetable for the Prime Minsiter’s departure by the chairman of the backbench 1922 Committee, Downing Street said Mrs May would be staying to see out the first phase of Brexit.
But briefing journalists after Prime Minister’s Questions, a Downing Street source said: "The Prime Minister made a very generous and bold offer to the 1922 Committee a few weeks ago that she would see through phase one of the Brexit process and she would leave and open up for new leadership for phase two.
"That's the timetable she is working towards. She wants to get Brexit done."
Taking questions from MPs, Mrs May also defended her record on Brexit after facing a blunt call to quit.
Tory backbencher Andrea Jenkyns told the Prime Minister that she had “failed” and said it was time to stand down.
"She's tried her best, nobody could fault or doubt her commitment and sense of duty, but she has failed,” the staunch Brexiteer said.
"The public no longer trust her to run Brexit negotiations. Isn't it time to step aside and let someone else lead our country, our party and the Brexit negotiations?"
Mrs May replied: "This is not an issue about me and it's not an issue about her. If it were an issue about me and the way I vote, we would already have left the European Union."
Last month, the executive decided by nine votes to seven against cutting the period between motions of no confidence in the party leadership, from one year to six months. The Prime Minister survived a coup attempt in December, and under current rules is safe from any challenge until the end of 2019.