Ahead of the vote, the Prime Minister said she would fight the vote "with everything I've got".
Candidates for the leadership must be nominated by two Conservative MPs.
She would be toppled if 158 of her party's 315 lawmakers don't support her in a ballot set to take place after 1 p.m. ET on Wednesday.
A confidence vote is triggered if 48 Conservatives write letters demanding one to the chairman of the party's so-called 1922 committee, Graham Brady.
Seeking to consolidate her position, May called an election in June 2017. Many had expected her to join the wave of resignations that followed the publication of May's draft withdrawal deal.Mordaunt said she backed May in the confidence vote.
Parliament has until January 21 to vote on the deal, a little more than two months before Britain's March 29 departure date.
"A leadership election would not change the fundamentals of the negotiation or the parliamentary arithmetic", May said in the House of Commons on Wednesday. It came just days after May postponed a vote to approve the divorce deal to avoid all-but-certain defeat.
European Commission President Jean-Claude Juncker is ruling out any renegotiation of the divorce agreement with Britain but says elements of the Brexit deal could still be clarified.
May's decision to pull the vote on her Brexit deal enraged MPs who oppose the accord she reached in Brussels.
Former Environment Secretary Owen Paterson accused May of acting like a "supplicant" in dealings with the EU.
Kate reveals Prince Louis has hit an adorable new milestone
As artificial snow fell, William chucked artificial snowballs at a children's entertainer, and Kate was caught in the crossfire. Kate previously wore the chic blazer by the label, which is also one of Meghan's favourites, during her tour of Canada in 2016.
The challenge against Mrs May has been brought by Conservative MPs who think she has watered down the Brexit that voters were promised in the 2016 referendum. The candidate with the fewest votes is removed and Conservative lawmakers vote again.
But May loyalist Chris Grayling, her transport minister, said the party had endorsed her "comfortably".
British business figures expressed alarm at the prospect of even more political uncertainty.
Adam Marshall, director general of the British Chambers of Commerce, said politicians should understand the impact of their "high stakes gambles" with Britain's economy. That's the 15 per cent of Conservative legislators needed to spark a leadership challenge under party rules. It's possible that under the newly centralised party membership system, a ballot could be held by email, but many members would want a postal vote.
Speaking outside 10 Downing Street after the leadership challenge was triggered on Wednesday morning, May insisted she was ready to face it.
May spoke at the weekend to Tusk, Merkel and Irish Prime Minister Leo Varadkar, raising speculation they offered some hope of further concessions. If she loses the vote, she will be replaced. But our party will rightly not tolerate it. But on Monday she pulled a parliamentary vote on her deal - which seeks to keep Britain closely aligned with the European Union after exit - to avoid defeat.
But Cabinet colleagues rallied to May's support. Home Secretary Sajid Javid tweeted that a leadership contest, with Brexit little more than three months away, "will be seen as self-indulgent and wrong".
"The size of the vote does matter", said polling expert John Curtice.
"There is no room whatsoever for renegotiation", Juncker told European Union lawmakers in Strasbourg, France, as he briefed them on Thursday's summit.
Since the resignation of former Brexit Secretary David Davis in the summer, May has come under increasing attack from cabinet colleagues, several of whom resigned in protest at her handling of negotiations with Europe, and a growing number of influential Conservative parliamentary members (MPs), who want to sever ties with the European Union without remaining in several key European Union arrangements.
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