Theresa May is awaiting the result of a vote by Conservative MPs on whether they want to keep her as their leader.
The UK prime minister made a last-minute appeal for support at an emotional meeting of backbench MPs.
She told them she will not lead the party into the next scheduled election in 2022 - but wants to stay on to deliver her Brexit deal, MPs said.
She faces a vote of confidence in her leadership after 48 Conservative MPs called for one to be held.
The majority of Conservative MPs have publicly said they will support the PM but it is a secret ballot and there were signs of nerves among party managers ahead of the vote in Committee Room 14 at the Palace of Westminster.
Voting finished at 20:00 with the result expected within the next hour.
The prime minister was greeted with applause, and the traditional banging of desks, as she went in to the committee room to address her MPs. Some of them were reported to be in tears.
She is understood to have promised not to call a "snap general election" and told MPs that in her heart she would have liked to have led them into the next scheduled election, partly because of what had happened at last year's election, when she lost her majority.
But, she added: "I realise that the party would like a different leader to take them into that election."
Cabinet minister Amber Rudd said "she was very clear that she wont be taking the general election in 2022".
But Jacob Rees-Mogg, a key figure in the campaign to oust Mrs May, said she had received a "half-hearted" reception from MPs.
She had said it was not her "intention" to fight the next election, added Mr Rees-Mogg, which he said was a "politician's word".
Powerful & moving moment in the #1922 as the PM makes clear that she has has listened, heard & respects the will of the Party that once she has delivered an orderly Brexit, she will step aside for the election of a new Leader to lead the reunification & renewal we need. Respect. https://t.co/oF9KizADEU— George Freeman MP (@GeorgeFreemanMP) December 12, 2018
Marcus Fysh, who also submitted a no confidence letter, said Mrs May "didn't really have anything new to say" about Brexit.
She vowed to involve more people in developing policy, the MP told BBC News, but he did not think that would happen.
And he predicted that the prime minister would face a no-confidence vote of all MPs - not just Conservative ones - when she tried to get her Brexit deal through the Commons.
"Whatever happens tonight I don't think she will be able to command the confidence of the House for the type of Brexit she is trying to pursue."
Minister Margot James said she was "proud" to have voted for the PM, tweeting a picture of her ballot paper.
Proud to have voted in support of the PM, thank you to the many people who have contacted my office today to urge me to do just that pic.twitter.com/pF5ChA4xHh— Margot James (@margot_james_mp) December 12, 2018
Conservative Party rules say that if she wins tonight she can stay on as leader, undisturbed, for another 12 months.
That takes one uncertainty off the table. But she would be weaker - lonelier - and with less authority to drive her Brexit compromise through.
Already, cabinet ministers are speculating about which way she can tack.
The parliamentary sums don't change on her current planned agreement with the EU. The cabinet, let alone the rest of the Commons, won't give their backing.
Can she survive the confidence vote?
Immediate statements of loyalty for the prime minister were issued by every member of her cabinet, including several who have been touted as possible successors.
Foreign Secretary Jeremy Hunt said Mrs May was "the best person to make sure we actually leave the EU on March 29", while Chancellor Philip Hammond suggested the vote would "flush out the extremists" in his party whose Brexit agenda was "not in the interests of the British people".
So far, 174 Tory MPs have publicly said they will vote for her, with 34 publicly against, according to BBC research. She needs to secure the votes of 159 MPs to survive.
If Mrs May wins the confidence vote she cannot be challenged as Conservative leader for at least another year.
If she does not win the vote there would then be a Conservative leadership contest in which she could not stand.
If Mrs May won - but not overwhelmingly - she may decide to stand down as party leader and trigger a leadership contest in which she could not stand.
What has Theresa May said?
In her statement delivered early on Wednesday morning, Mrs May said: "A leadership election would not change the fundamentals of the negotiation or the Parliamentary arithmetic.
"Weeks spent tearing ourselves apart will only create more division just as we should be standing together to serve our country. None of that would be in the national interest."
She said she was making progress in her talks with EU leaders and vowed to "deliver on the referendum vote and seize the opportunities that lie ahead".
The Conservatives had to build a "country that works for everyone" and deliver "the Brexit people voted for".
"I have devoted myself unsparingly to these tasks ever since I became prime minister and I stand ready to finish the job."
Will there be a new prime minister if she loses the vote?
Not immediately. She would be expected to stay on as a caretaker prime minister until a new Conservative leader is selected by the party, a process that could take up to six weeks.
If there are multiple candidates, Conservative MPs hold a series of votes to choose two to go forward to a vote of party members.
As leader of the largest party in the Commons, the new Conservative leader would then be expected to be asked to form a government and become prime minister, without a general election.
It's Wednesday, so... Prime Minister's Questions
Mrs May faced repeated calls from Labour MPs for her to quit - or hold another EU referendum - at a rowdy Prime Minister's Questions.
Labour leader Jeremy Corbyn said: "The time for dithering and delay is over. The prime minister has negotiated her deal. She has told us it is the best and only deal available.
"There can be no more excuses, no more running away. Put it before Parliament and let's have the vote."
Mrs May said the vote will take place, and as Labour MPs shouted "when?" at her she said: "We've had a meaningful vote, we had it in in the referendum in 2016."
The PM added: "And if he wants a meaningful date I'll give him one; 29 March 2019 when we leave the European Union."
Veteran pro-European MP Ken Clarke called the prospect of a leadership contest "unhelpful, irrelevant and irresponsible", prompting loud cheers from the Tory benches.
But the SNP's leader at Westminster Ian Blackford called on Mrs May to stand down, saying her government was "an embarrassment".
Who is trying to oust Mrs May?
The challenge has been brought by Conservative MPs who think Mrs May has watered down the Brexit voters were promised in the 2016 referendum.
The PM thought she had seen off an attempt by this group of Brexiteers to get rid of her last month.
But her decision to cancel Tuesday's Parliamentary vote on her deal at the last minute proved to be the final straw for many who had previously given her the benefit of the doubt.
There needed to be 48 MPs calling for her to go - out of 317 Conservative MPs - to trigger a confidence vote and this threshold was reached on Tuesday.
Jacob Rees-Mogg, who has led backbench calls for her to go, said: "Theresa May's plan would bring down the government if carried forward. But our party will rightly not tolerate it.
"Conservatives must now answer whether they wish to draw ever closer to an election under Mrs May's leadership. In the national interest, she must go."
And Bernard Jenkin said the survival of the Conservative government depended on the support of the Democratic Unionists, who he said had lost faith in Mrs May.
Conservative MP Sarah Wollaston, who is campaigning for a further referendum, told BBC Radio 2 she hoped Mr Rees-Mogg's group would "get a kicking" in the vote and that their "pompous gesturing" will be exposed.
Why are they trying to get rid of her?
They don't like the deal she has struck with the EU, which they say will keep the UK tied to the EU indefinitely with no say over its rules and unable to strike trade deals around the world.
Anger has focused on the so-called "backstop" to prevent the return of a physical border in Northern Ireland.
Mrs May has said she is seeking guarantees that this clause will be "temporary" but the Democratic Unionist Party, which she relies on to win key votes, wants the backstop to be ditched altogether.
And her Conservative critics think she will not be able to get anything more than cosmetic changes to her withdrawal deal because EU leaders say it can not be renegotiated.
Who are the frontrunners to lead the party if she loses?
There are many names being floated, with Home Secretary Sajid Javid, Foreign Secretary Jeremy Hunt, Environment Secretary Michael Gove and Work and Pensions Secretary Amber Rudd among cabinet ministers rated by the bookmakers.
Former Brexit Secretary Dominic Raab, ex-Foreign Secretary Boris Johnson and ex-Brexit Secretary David Davis are the ex-cabinet ministers also judged to be in the running.
But, as BBC political editor Laura Kuenssberg says, the field of hopefuls could be much larger and, initially at least, resemble the start of a Grand National.
What does it mean for Brexit?
Whatever the outcome of the vote, Mrs May is still likely to represent the UK at Thursday's summit of EU leaders, although that might change if she loses the Tory leadership.
She has been invited to update her 27 counterparts on the state of Brexit before they meet to "adopt relevant conclusions".
European Council President Donald Tusk has said the "seriousness" of the situation in the UK means the EU must accelerate its no-deal planning.
Mrs May met Germany's Angela Merkel and top EU officials on Tuesday as part of efforts to get changes to her EU deal to get it through the UK Parliament.
But she was forced to call off talks with Irish premier Leo Varadkar, among others, on Wednesday to fight for her leadership.
Mrs May says any new Conservative leader would have to delay Brexit to renegotiate a deal with the EU while she has also suggested a leadership contest will effectively hand control of the Brexit process to MPs - many of whom either back leaving without a deal or having another referendum.
Many of those calling for her to go say they would be happy for the UK to leave the EU on World Trade Organization terms, without a deal. They say warnings of economic doom are exaggerated.