LONDON – British Prime Minister Theresa May offered Wednesday to step aside to break a deadlock over her unpopular plan to leave the European Union.

May said she would not stay on as prime minister once the country left the EU. She didn’t set a departure date. May has been Britain's leader since 2016.

The vow to quit was made to persuade lawmakers to support her EU exit deal.

"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 told lawmakers from her Conservative 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," she told the 1922 Committee, an influential group of lawmakers.

The EU withdrawal deal May agreed to with European leaders was rejected twice by British lawmakers because they said it wouldn't do enough to disentangle Britain from the EU. British parliamentarians started voting this week on a series of options related to Britain’s break from the EU, known as Brexit.

These options include reversing Brexit and leaving the bloc without a final divorce deal. Economists said the latter scenario risks serious harm to Britain’s economy and could lead to travel chaos and shortages of essential medicines.

The process could extend into next week, but May hinted that she wanted to bring her controversial deal back to Parliament by Friday. No decision has been made.

Late Wednesday, lawmakers failed to find a majority for any alternative Brexit arrangement to May’s Brexit deal, but agreed by an overwhelming majority that they opposed leaving the bloc without any agreement.

Some lawmakers said they would back May’s deal only if she announced a date to step down. The EU gave Britain until April 12 to come up with an alternative Brexit plan if May was not able to get her deal with the EU through Parliament.

Anna Soubry, a former Conservative lawmaker who left May's party to join a breakaway cross-party group known as the Independent Group, criticized what she said were hard-line pro-Brexit voices drowning out May.

Even if May's deal passes, the Brexit process wouldn't be over. The deal she is trying to get through Parliament is just a transition-period arrangement. Her successor would need to negotiate post-EU trade deals and oversee other aspects of British legislation pertaining to life outside the bloc from public health to security policy.

"So hard Brexiteers will vote for the PMs 'deal' not because it’s good for our country and the right thing to do – not even because it delivers Brexit but because it gets rid of the PM #Shameful," Soubry wrote on Twitter.

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Unlike in the USA, Britain does not elect a leader. It elects a party. This means that when May leaves office, her ruling Conservative Party will still be in power as long as it can agree on who should replace her. If it can't, there will be an election.

May, 62, won her leadership role in the aftermath of David Cameron's resignation in 2016. He stepped down after miscalculating that Britain would vote to stay in the EU.

May is Britain's second female prime minister after Margaret Thatcher (1979-90) and made a name for herself while serving in Cameron's Cabinet as home secretary. In that role, she took a strict line on drug policy, immigration and fighting terrorism.

There are no out-and-out front-runners to succeed her, although one name that is never far from political scientists' short lists is Boris Johnson, 54, the gaffe-prone former mayor of London and ex-foreign secretary.

Johnson is known for his colorful rhetoric, unashamed support for Brexit and love of Winston Churchill. In a USA TODAY interview in 2014, New York-born Johnson said his chance of becoming Britain's prime minister was about as good as finding Elvis on Mars or being reincarnated as an olive.