Mrs May assured mutinous Tory MPs she will resign as Prime Minister ahead of the next general election if they back her to deliver Brexit.
“I won't lead the party into the next general election,” Mrs May said, according to a Tory MP present at the meeting.
Ministers were reportedly reduced to tears when the PM said it is “not her intention to lead the party into the 2022 election” in what has been described as an “emotional meeting”.
The assurance is aimed at gaining the backing of Tory MPs who wish to avoid instability but did not want her to lead the party into the next election.
When asked when she intends to resign, however, Mrs May “ducked” the question despite calls for her to stand down after the Brexit deadline on March 29, 2019.
Tory vice-chairman James Cleverly told reporters: "She said this would be a very, very bad time to change leader. She made it clear theres a job to be done.”
1922 COMMITTEE: Live images of Tory MPs at the behind-closed-doors meeting (Pic: SKY NEWS)
Cabinet minister Amber Rudd told reporters: "She's made the commitment that I think is what people wanted, but she was very clear that she wont be taking the general election in 2022."
Tory MP George Freeman said Mrs Mays “powerful” and “moving” speech shows she has “listened, heard and respects” the will of the party for her to step aside.
Arch Brexiteer Jacob Rees-Mogg, on the other hand, was not convinced by her performance, casting doubt on her vow to resign.
He said: “The PM hedged her bets on the question of leading the party into the 2022 election – she said she had no intention, but the word intention is a classic politicians word, because it can change.”
The PM delivered the make-or-break speech to Tory MPs who will decide her fate at a behind-closed-doors meeting of the 1922 Committee in the House of Commons.
Conservative MPs have started casting their votes in the confidence ballot on her leadership.
With anticipation mounting, Tory MPs theatrically banged on desks as she arrived to deliver the speech of her political life.
MOMENT OF TRUTH: Theresa May has addressing MPs at the 1922 Committee (Pic: GETTY)
Within the next few hours the 317 Tories will cast ballots before the result is announced at around 9pm.
Amid widespread dissatisfaction with her Brexit deal, Tory MPs will decide whether to oust Mrs May after submitting 48 letters to the 1922 Committee.
Announcing the leadership challenge this morning, the PM vowed to give “everything Ive got” to put down the rebellion staged by what chancellor Philip Hammond called Eurosceptic “extremists”.
In a telling admission, a spokesman for Downing Street said the confidence vote tonight is “not about who leads the party into the next election”, suggesting she could stand aside at some point.
FIGHTER: Mrs May vowed to give 'everything I've got' to win the no confidence vote (Pic: GETTY)
Yet, despite fierce opposition to her Brexit deal, more than 150 Tory MPs have publicly declared their support for Mrs May, suggesting she could coast to victory in the no confidence vote.
However, the Tories are keen for her to make way for another leader when Brexit had been completed.
The PMs spokesman said: “She is fighting for every vote. We have seen support from across the parliamentary party this morning but there is a lot more to do this afternoon.
"This vote isnt about who leads the party into the next election, it is about whether it makes sense to change leader at this point in the Brexit process."
The PM needs the support of at least 158 of her MPs to remain party leader.
EMOTIONAL PLEA: Ministers were reportedly reduced to tears by Mrs May's speech (Pic: PA)
A failure to reach enough support to stay on as PM would trigger a leadership contest in which Mrs May could not stand.
However if she wins, another challenge cannot be made against her for a year, giving her more time to deliver Brexit based on her deal.
Many of her her supporters see the no confidence vote as an opportunity to “put a stake into the heart” of the European Research Group (ERG), which is led by arch Brexiteer Tories Jacob Rees-Mogg and Steve Baker.
In a statement outside 10 Downing Street on Wednesday morning, Mrs May warned a change of leadership would put the UK's future at risk and could delay or halt Brexit.
“This vote isnt about who leads the party into the next election”
Downing Street spokesman
Mrs May was buoyed by cheers from her own backbenches in a raucous House of Commons as she stood up for what could be her final session of PMQs.
Husband Philip showed his support by watching from the public gallery, while Tory elder statesman Kenneth Clarke told MPs that a leadership contest within months of the March 29 date of Brexit would be "irresponsible and unhelpful".
Mrs May resisted calls from Labour and the Scottish National Party to bring her Brexit deal immediately back before the Commons, after she pulled the "meaningful vote" expected on Tuesday.
And she insisted a general election would not be "in the national interest".
Labour leader Jeremy Corbyn denounced her actions as "totally and absolutely unacceptable", while the SNP's leader in Westminster Ian Blackford called on her to resign.
PMQS: Mrs May warned Brexit will need to be delayed if she loses the vote (Pic: GETTY)
Ministers touted as possible successors to the PM were among those voicing support for her.
Foreign secretary Jeremy Hunt said Mrs May is "the best person to make sure we actually leave the EU on March 29", while home secretary Sajid Javid said a leadership contest would be seen as "self-indulgent and wrong".
But in a joint statement, Jacob Rees-Mogg, chairman of the ERG, 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."
LETTERS SUBMITTED: Graham Brady, chairman of the Conservative Party 1922 Committee (Pic: GETTY)
Mrs May cleared the decks to lobby Tory MPs for their backing, cancelling a planned meeting of cabinet and a trip to Dublin for talks with Irish premier Leo Varadkar.
Labour Party chairman Ian Lavery said: "With only weeks left before Britain leaves the EU, Theresa May's weakness and failure has completely immobilised the Government at this critical time for the country.
"The Prime Minister's half-baked Brexit deal does not have the backing of her Cabinet, her party, Parliament or the country.
"The Conservative Party's internal divisions are putting people's jobs and living standards at risk."