Theresa May is due to meet senior Conservative MPs who are demanding she sets a date for her departure from Downing Street.
The PM, who is under growing pressure from her own MPs to stand aside, will meet the executive of the backbench 1922 Committee to discuss her future.
Existing rules mean she cannot be formally challenged until December.
Mrs May has said her departure depends on delivering Brexit, but her plan has been rejected by MPs three times.
A further attempt to progress with her plan will take place in the week beginning 3 June, when the withdrawal bill – required to implement the PM’s Brexit deal – will be considered by MPs.
But, when asked whether she would resign if this was rejected by MPs, Mrs May said the bill would “ensure that we deliver Brexit for the public”.
Senior Conservative MPs are expected to press her to set out her departure timetable, regardless of whether Parliament backs her Brexit withdrawal agreement.
After the talks with the prime minister, the executive will hold another meeting where changes to the leadership rules could be discussed again.
Last month, the 1922 Committee executive narrowly decided against changing the party’s leadership rules to allow an early challenge to Mrs May.
Theresa May’s very long goodbye
Twice my colleague in Paris asked the prime minister if she would resign if her Brexit plan is rejected by MPs again. Twice she completely swerved the question.
You can’t blame her for wanting to avoid it. Theresa May is not exactly fond of revealing much in interviews in any case.
And for her to go anywhere near tangling with her potential exit would have breathed even more fire into the frenzied speculation.
But it is notable that the prime minister didn’t even repeat any of her rehearsed lines about her promise to see this phase of Brexit through, and then go.
Pressure has grown on Mrs May since the Tories’ local election drubbing earlier this month and much of the anger in the parliamentary party is focusing on Mrs May’s efforts to find a Brexit compromise with Labour.
Further pressure has also emerged from the grassroots, with local Tory associations confirming they will hold a vote of confidence in her leadership on 15 June.
Eurosceptic MP Peter Bone produced a letter from Tory activists in the Commons on Wednesday, saying they had lost confidence in the prime minister and want her to resign before European elections on 23 May.
They view the deal that Mrs May has reached with the EU as “worse than staying in the European Union”, he said.
And Mrs May’s former chief of staff, Nick Timothy, writing in his Telegraph column, said the prime minister must “accept that the game is up”.
She should “do her duty and stand aside” in order to avoid a “national humiliation” and save the Conservative Party, he said.
Sir Geoffrey Clifton-Brown, treasurer of the 1922 Committee, said: “What I would like to see is her set out a timetable to trigger a leadership contest.”
He said it would be “infinitely preferable if she set a date rather than us force her out”.
Prominent Brexiteer Mark Francois said a predicted poor performance by the Conservatives in next week’s European Parliament elections would increase the pressure on Mrs May to stand down.
“As the polls increasingly suggest, we are going to have an extremely difficult night in the European elections,” the MP said.
When the results are announced, “my colleagues will finally wake up and smell the coffee if they have not, indeed, done so already,” he added.
But International Development Secretary Liam Fox told BBC Radio 4’s Today programme that the prime minister’s pledge to stand down when the first stage of Brexit is through showed “integrity” as “she was willing to make that personal sacrifice to get the policy through”.
He said MPs had been given an instruction by the British public through the 2016 referendum, asking: “Why have they not carried it out?”
Brexit Secretary Stephen Barclay told MPs their concerns had been listened to and that was “reflected in the draft legislation that is being prepared”.
“It will be for members of this House to reach a decision between that (the withdrawal agreement bill) and the two other alternatives, which is either we risk not leaving at all… or we leave with a no deal,” he said.
However, shadow Brexit secretary Keir Starmer said Labour opposed the idea of passing the bill without an agreed deal, as it would “put the cart before the horse”.
He questioned whether the planned introduction of the bill was “about keeping the prime minister in office for another week, to give her a lifeline” ahead of the 1922 Committee executive meeting.