Theresa May has vowed to fight a vote of no confidence from Conservative MPs "with everything I've got".
The ballot will be held on Wednesday evening after the threshold of letters from Tory MPs needed to trigger the contest was exceeded.
In a statement outside 10 Downing Street, the prime minister said she was ready to "finish the job" she set out on when she became leader.
And she warned ousting her would "put our country's future at risk and create uncertainty when we can least afford it" and could lead to Brexit being delayed or prevented.
Mrs May said: "We must and we shall deliver on the referendum vote and seize the opportunities that lie ahead."
ITV News Political Editor Robert Peston said Mrs May's attempt to be seen as "the personification of Brexit" risked uniting Brexiters and Remainers against her.
Sir Graham Brady, the chairman of the backbench 1922 Committee, said the threshold of 48 letters - 15% of the parliamentary party - needed to trigger a vote has been reached and a ballot will be held between 6pm and 8pm on Wednesday evening in the House of Commons.
The votes will be counted immediately afterwards and the result will be announced "as soon as possible" - expected to be around 9pm.
Immediate statements of loyalty for the Prime Minister were issued by Cabinet ministers, including several who have been named as potential contenders to be her successor
Mrs May needs to secure the votes of 158 MPs - half the parliamentary party plus one - to remain as Conservative leader, though a vote of 100 or more against her will raise questions about whether she can continue.
If she wins, another challenge cannot be mounted against her position as Tory leader for a year.
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At Prime Minister's Questions, Labour leader Jeremy Corbyn focused more on Mrs May's decision to pull a Commons vote on her Brexit deal, saying only that the no-confidence vote was "utterly irrelevant" to the lives of people around the country.
During PMQs, Conservative MP Ken Clarke was cheered as he asked Mrs May if she could "think of anything more unhelpful, irrelevant and irresponsible" than a Conservative Party leadership contest "at a time of grave national crisis".
She responded by repeating her warning that after weeks of leadership campaigning, one of the first things a new leader would have to do would be to "delay or stop Brexit".
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Sir Graham said he spoke with Mrs May on the phone on Tuesday night and she was "very keen that the process is concluded as quickly as reasonably possible".
He added: "I don't suppose it was a surprise but obviously it was important to wait until there was confirmation that the process was actually triggered".
Former Brexit Secretary David Davis, who resigned over the Brexit deal, told ITV News he would be voting "in the national interest" but will wait until Mrs May has addressed Conservative MPs this evening before deciding how he will vote.
Justice Secretary David Gauke said a leadership election would create "huge uncertainty" at a crucial moment.
He told ITV News that if Mrs May was removed from office Brexit could be delayed by at least six months.
"If there is a change of leader voted for tonight then there is little or no choice but to delay Article 50 taking effect," he said.
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There were reports on Tuesday of a wave of new letters amid anger at the way Mrs May dramatically put on hold the crunch Commons vote on her Brexit deal after admitting she was heading for a heavy defeat.
Speculation that a challenge could be imminent was fuelled after chief whip Julian Smith and Conservative Party chairman Brandon Lewis were seen leaving No 10 following late-night consultations on Tuesday.
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In a joint statement, the chairman of the pro-Brexit Conservative European Research Group Jacob Rees-Mogg and his deputy Steve Baker 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."
Former Prime Minister David Cameron, who resigned after the 2016 referendum, tweeted his support for Mrs May.
"We need no distractions from seeking the best outcome with our neighbours, friends and partners in the EU," Mr Cameron said.
What did Theresa May say?
Standing before the famous door to Number 10, a defiant Mrs May said: "Sir Graham Brady has confirmed that he has received 48 letters from Conservative MPs so there will now be a vote of confidence in my leadership of the Conservative Party.
"I will contest that vote with everything I've got."
Mrs May said securing a Brexit deal which will deliver on the result of the 2016 referendum is "now within our grasp", and added she is "making progress" in securing reassurances from EU leaders on MPs' concerns about the proposed backstop for the Irish border.
But she warned: "A change of leadership in the Conservative Party now would put our country's future at risk and create uncertainty when we can least afford it."
A new leader could not be in place by the January 21 deadline by which the PM must confirm an agreement in principle had been reached with Brussels on a Brexit deal, she said.
"A leadership election risks handing control of the Brexit negotiation to opposition MPs in Parliament," she said.
"The new leader wouldn't have time to renegotiate a withdrawal agreement and get the legislation through Parliament by March 29, so one of their first acts would have to be extending or rescinding Article 50 - delaying or even stopping Brexit when people want us to get on with it."
Theresa May speaks in Downing Street.
Theresa May speaks in Downing Street. Credit: PA
A leadership election "would not change the fundamentals of the negotiation or the parliamentary arithmetic", she said.
"Weeks spent tearing ourselves apart would only create more division, just when we should be standing together to serve our country. None of that would be in the national interest.
"The only people whose interests would be served are Jeremy Corbyn and John McDonnell."
Mrs May said she wants to focus on voters' priorities like the economy, public services and housing, as well as delivering on the referendum vote.
She said she has devoted herself "unsparingly" to delivering her agenda of "building a country that works for everyone" since becoming PM, adding: "I stand ready to finish the job."
Mrs May said she had cancelled a planned trip to Dublin on Wednesday evening for talks with Irish Taoiseach Leo Varadkar in order to "make the case for my leadership" with MPs.
She is expected to speak with individual Tory MPs during the day before addressing the 1922 Committee at 5pm, immediately before the crucial vote.
Ministers rally round the PM
Several Cabinet minister quickly rallied round Mrs May following news of the vote, including several who have been named as potential contenders to be her successor.
Jeremy Hunt, Sajid Javid, Michael Gove, Philip Hammond, Matt Hancock, Penny Mordaunt, Liam Fox, Steve Barclay, David Lidington, Amber Rudd, Chris Grayling, David Gauke and James Brokenshire were among those making statements of support.
Foreign Secretary Mr Hunt tweeted that he was backing Mrs May to stay in the job, while Work and Pensions Secretary Ms Rudd said MPs "need to support and work with the PM".
Home Secretary Mr Javid said the contest was "the last thing our country needs right now" and that it would be seen as "self-indulgent and wrong".
https://www.itv.com/news/2018-12-12/conservative-leadership-theresa-may/