In a meeting with legislators from her Conservative party on Wednesday, May said she would quit if the twice-defeated divorce deal she negotiated with the European Union passes at a third vote.
“We need to get the deal through and deliver Brexit,” May said, according to a statement released by her office.
“I am prepared to leave this job earlier than I intended in order to do what is right for our country and our party.”
It is the first time May has acknowledged she is prepared to quit in order to secure the votes for her Brexit deal to pass.
Britain was due to leave the European Union on March 29 but has been granted a delay until April 12, after parliament overwhelmingly rejected May’s divorce deal on two occasions.
“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,” she said.
She did not set a date for her departure.
The announcement comes as MPs debate alternative approaches to Brexit in the House of Commons.