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May was forced to make the offer to Conservative party lawmakers in an attempt to persuade them to back her twice-rejected EU withdrawal deal.
Her gambit came as British lawmakers prepared to vote on alternatives to her plan in an unprecedented debate after her government lost control of Wednesday's parliamentary timetable.
She told the 1922 Committee, the influential group of all backbench Conservative Members of Parliament, that she will make way for another Conservative leader so that lawmakers could complete their "historic duty" and "deliver on the decision of the British people and leave the European Union with a smooth and orderly exit."
"I am prepared to leave this job earlier than I intended in order to do what is right for our country and our party," May said on Wednesday according to excerpts of her speech released by Downing Street.
"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."
Conservative Party lawmaker Simon Hart said of May: "She has said that she will not stay through to the next phase of negotiations. If they (MPs) back the deal she will go."
"No timescale was talked about or given," Hart told CNN. "The implication was if she gets her deal through, that will kick start the process to find a new leader almost immediately."
He added that the atmosphere was "respectful" and May "was as animated as I'd ever seen her at committee. She was passionate but not emotional. We are all traumatized at this point by these negotiations."
Parliamentary arithmetic
Lawmakers reacted to the news on Twitter, including Anna Soubry, who recently left the party to join a breakaway cross-party bloc known as the Independent Group. She tweeted that it was "shameful" that "hard Brexiteers will vote for the PMs 'deal' not because it's good for our country and the right thing to do ... but because it gets rid of the PM."
