British Prime Minister Theresa May said Wednesday she will step down if Parliament approves her twice-defeated deal for the United Kingdom to leave the European Union.

"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, as the government is considering bringing the Brexit deal back to the House of Commons for a third vote possibly on Friday.

May had promised to step down before the next general election slated for 2022. By agreeing to leave sooner, she sought to increase the chance of her unpopular deal passing.

Last week, EU leaders agreed with the prime minister to extend the deadline for Britain's departure from the European Union to May 22, provided that British lawmakers pass a withdrawal agreement by Friday.

(Theresa May leaves Parliament)[Getty/Kyodo] 

If May does succeed in passing her Brexit deal, she is hoping for a final appearance on the world stage as prime minister at a Group of 20 summit in late June in Osaka, Japan, with a successor to be installed before the summer break, the Financial Times reported.

Bookmakers put Michael Gove, the environment secretary, and Boris Johnson, a former foreign secretary, as the front-runners, the paper said.

In a meeting of Conservative Party lawmakers on Wednesday, May tried to persuade rebels in her party to support her withdrawal agreement. But the prime minister did not touch on the date of her departure.

"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, according to a transcript released by her office.

"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."

May has faced growing pressure from within her Conservative Party to resign or give a date for her resignation after Parliament twice rejected her agreement with the European Union on the terms of Britain's departure, initially scheduled for March 29.