Speaking in Downing Street after it was announced that she will face a vote of confidence this evening, the Prime Minister said a change in leadership would "put our country's future at risk and create uncertainty when we can least afford it".
A secret ballot of Conservative MPs will take place between 6pm and 8pm on Wednesday, the chairman of the Conservative backbench 1922 Committee, Sir Graham Brady confirmed after revealing he had received the 48 letters of no confidence from Tory MPs required to trigger a ballot on the leadership.
The Prime Minister must secure 158 votes to stay in her post, but would be severely weakened if more than 100 MPs chose to oust her.
Mrs May insisted she would stay on to "finish the job" she has set herself as Prime Minister, and warned that a new leader would not have time to renegotiate her deal with Brussels.
That would risk handing the EU control of the Brexit process, and could mean the UK's departure is delayed or even cancelled, she said.
"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," Mrs May said.
"A new leader wouldn’t be in place by 21 January legal deadline, so a leadership election risks handing control of the Brexit negotiations to opposition MPs in parliament.
"The new leader wouldn’t have time to renegotiate the withdrawal agreement and get the legislation through parliament by 29 March, 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.
"And 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."
Mrs May added: "None of that would be in the national interest. The only people whose interests would be served would be Jeremy Corbyn and John McDonnell."