Theresa May told Conservative Party MPs on Wednesday that she would quit if her twice-defeated Brexit deal gets approved by parliament.
The Prime Minister said that she "will not stand in the way" of the party having new leadership for the second phase of Brexit negotiations.
She told the 1922 Committee: "I am prepared to leave this job earlier than I intended in order to do what is right for our country and our party."
A Tory MP said that while she didn't give a date, the impression was that she would go "reasonably soon".
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According to excerpts released by Downing Street, May told the committee: "I have heard very clearly the mood of the parliamentary party. I know there is a desire for a new approach - and new leadership - in the second phase of the Brexit negotiations - and I won't stand in the way of that.
"I know some people are worried that if you vote for the Withdrawal Agreement, I will take that as a mandate to rush on into phase two without the debate we need to have. I won't - I hear what you are saying.
"But we need to get the deal through and deliver Brexit."
She added: "I am prepared to leave this job earlier than I intended in order to do what is right for our country and our party.
"I ask everyone in this room to back the deal so we can complete our historic duty - to deliver on the decision of the British people and leave the European Union with a smooth and orderly exit."
Speaking as he left the meeting in Westminster, Tory MP James Cartlidge said: "My recollection is that she said she would not remain in post for the next phase of the negotiations, the implication being that once the Withdrawal Agreement has passed, she would make way for someone else."
First Minister Nicola Sturgeon tweeted: "If Brexit ends up being forced through on the basis of a deal no one supports - indeed a deal so bad that the PM has to promise to resign to get it through - it will make an already bad project even worse."
