Prime Minister Theresa May has said she will not lead the Conservative Party into the next general election.
She said the party would prefer to "to go into that election with another leader", as she arrived in Brussels for an EU summit.
It confirms what she told MPs ahead of a confidence vote triggered by MPs angry at her Brexit policy.
Theresa May won the vote but has vowed to listen to the concerns of the 37% of Tory MPs who voted against her.
The next scheduled general election is in 2022.
Theresa May said: "I've said that in my heart I would love to be able to lead the Conservative Party into the next general election but I think it is right that the party feels that they would prefer to go into that election with another leader."
BBC political editor Laura Kuenssberg said that pre-announcing their departure tends to lead to power "draining away" from leaders, adding that the party's "rival tribes might be now set on a course to pull her - and themselves - apart" with the expectation that at "some point she will have to change tack on Brexit".
She said she hoped to "assuage" the concerns of Tory MPs who voted against her by seeking legal "assurances" from EU leaders that the backstop plan to prevent the return of a hard border in Northern Ireland would be temporary.
Critics say Theresa May's backstop plan will keep the UK tied to EU rules indefinitely and curb its ability to strike trade deals.
The EU says it will not renegotiate the backstop, but may agree to give greater assurances on its temporary nature.
It seems unlikely that would win over enough support for her Brexit plan to have a realistic chance of getting through the House of Commons, with tensions heightened in the Conservative Party in the wake of Wednesday evening's confidence vote.
Theresa May won the ballot of Conservative MPs, on whether she should remain their party leader, by 200 votes to 117,
May's message as she arrived in Brussels
Theresa May said she had listened to the concerns of the MPs who had voted against her, adding that she knew what was needed to get her deal "over the line".
"I've already met [Irish Premier] Leo Varadkar, I'm going to be addressing the European Council later and I'll be showing the legal and political assurances that I believe we need to assuage the concerns that MPs have on this issue."
She added: "I don't expect an immediate breakthrough but what I do hope is that we can start work as quickly as possible on the assurances that are necessary."
What was the EU's response?
Austrian Chancellor Sebastian Kurz, whose country holds the rotating six-month presidency of the European Council, said: "I believe that Theresa May knows that there can be no reopening of the withdrawal agreement."
But he said that it might be possible to "provide a little better explanation or definition or go into detail" on the provisions of the agreement.
"Hopefully that will allow Theresa May to bring a vote in January and obtain a majority," he said.
"If the British prime minister thinks one or another additional explanation can be helpful before she brings it to a vote, then we should do that."
Asked what concessions might succeed in winning over Theresa May's domestic critics, Mr Kurz said: "It is difficult to judge, because many of the sceptics do not argue in a way that is really rational."
What will happen at the EU summit?
Earlier this week, the prime minister travelled to meet EU leaders, including German Chancellor Angela Merkel and Dutch Prime Minister Mark Rutte, to raise the issues surrounding the withdrawal agreement at Westminster one-on-one.
But a trip to meet the Irish Taoiseach Leo Varadkar had to be cancelled because of the leadership vote.
At Thursday's summit, Theresa May has the opportunity to spell out face-to-face the problems she faces to leaders of all the other 27 member states.
The EU leaders will then consider what could be done - without Theresa May in the room.
'Brutal reality of no workable Brexit'
Theresa May will front up in Brussels - still the prime minister, still officially in charge.
One cabinet minister last night told me the whole challenge to her had been "futile", suggesting it hadn't really changed much.
But it really has. Theresa May has a temporary shield from another direct call for her departure from her own MPs . Angry Brexiteers can't try to move her out for another year in the same way.
That on its own is a sigh of relief certainly for her supporters, claiming a "good result" last night.
But that does not remotely protect her from the brutal reality that she, right now, has no workable Brexit policy that can make it through the Commons.
Any reassurances offered to Theresa May could centre on an attempt to "detoxify" the idea of the backstop for Westminster, says the BBC's Europe correspondent Kevin Connolly.
He said its temporary nature could be emphasised, along with the EU's readiness to keep searching for a better alternative even if the backstop were ever to be triggered - both stronger reassurances to the policy's critics than offered in the past.
For example, a draft of the European Council conclusions on Brexit says the EU would use its "best endeavours to negotiate and conclude expeditiously a subsequent agreement that would replace the backstop so that it would only be in place for a short period and only as long as strictly necessary".
In other words, the EU would continue trying to negotiate a trade deal with the UK even if the Irish backstop had been triggered at the end of the transition period. The Brexit withdrawal agreement only talks about "best endeavours" being used to reach an agreement during the transition period.
But the BBC's Brussels reporter Adam Fleming says the draft put forward by the European Council could be subject to change.
Westminster critics of Theresa May's Brexit deal might also complain that it is not legally binding.
However, the core message from Brussels remains that there will not be a renegotiation of the withdrawal agreement whatever happens, even if the Conservative Party had changed its leader.
This was reiterated by the President of the European Commission Jean-Claude Juncker who, in a phone call with Mr Varadkar on Wednesday, said that the deal on the table was "a balanced compromise and the best outcome available", and "cannot be reopened or contradicted".
What is being said in Westminster?
Tory MP Iain Duncan Smith, a former party leader and a Brexiteer who voted against Theresa May in Wednesday's vote, said he wanted to "send a strong message" to the PM.
He told BBC Radio 4's Today programme: "We cannot go on just with the idea that a fiddle here and a fiddle there is what the problem is."
Instead, he said Theresa May should say that the £39bn the UK has agreed to pay the EU as part of the divorce deal is "at risk".
"They have got to say to the EU... we are not committed to this £39bn unless we get some resolution."
Meanwhile it is still not clear when MPs will get their "meaningful vote" on Theresa May's Brexit deal, after it was called off earlier this week when she admitted it would have been "rejected by a significant margin".
Parliamentary business for next week has been set out but it does not include any "meaningful vote" - Parliament rises for Christmas recess on 20 December and is due to return on 7 January. Asked when it would be held, Commons Leader Andrea Leadsom said only that the debate and vote would be held "at the latest by the 21st January".
Lib Dem leader Sir Vince Cable, who is against Brexit, told BBC Breakfast: "We are still back with the problem that the government has a proposal that we can't get through Parliament and we have got to try and break that gridlock."
He called on Labour leader Jeremy Corbyn to "come off the fence" and back another public vote on Brexit.
Labour has said that it will table a no-confidence motion in Theresa May's government that all MPs - not just Conservatives - will be able to vote in - but only when they felt they had a chance of winning it, and forcing a general election.
But the DUP - which props up Theresa May's government - said it would not support such a motion at this stage.
Shadow Chancellor John McDonnell urged Theresa May to work with Labour on getting a deal with the EU that "will protect jobs and the economy".
He said there was an "overwhelming majority" in the Commons against a no-deal Brexit but the prime minister should now hold a series of votes to establish what other options MPs were willing to accept.
What happened at the confidence vote?
The prime minister won the confidence vote with a majority of 83 - 63% of Conservative MPs backing her and 37% voting against her.
Her supporters urged the party to move on but critics said losing the support of a third of MPs was "devastating".
The BBC's Laura Kuenssberg said the level of opposition was "not at all comfortable" for the prime minister and a "real blow" to her authority.
A split was still clear in the Tory party after the result. Jacob Rees-Mogg, who led calls for the confidence vote, said losing the support of a third of her MPs was a "terrible result for the prime minister" and he urged her to resign.
But Nicholas Soames urged Brexiteers to "throw their weight" behind the PM as she sought to address the "grave concerns" many MPs had about aspects of the EU deal.
DUP deputy leader Nigel Dodds said his party was also still concerned about the Irish backstop plan, telling BBC News: "I don't think this vote really changes anything very much in terms of the arithmetic."