Theresa May is to meet the chairman of the Tory party’s influential 1922 Committee amid backbenchers’ calls for her to set a firm resignation date.
The prime minister’s meeting with Sir Graham Brady comes after the 1922 Committee requested "clarity" about her timetable for standing down and triggering a leadership contest.
As talks between the government and Labour over a Brexit deal resume on Tuesday, there is growing Tory pressure for Mrs May to quit.
Leading Eurosceptic Sir Bill Cash said: "The time has come for her to resign.
"She needs to be given a date. The sooner the better. But it needs to be done in an orderly manner."
The comments came as the Daily Telegraph reported that grassroots Tories will hold a no-confidence vote in Mrs May on June 15.
The vote by members at an EGM of the National Conservative Convention would not be binding, but would add pressure on Mrs May to quit if passed.
Brexit Party leader Nigel Farage said: "I'm amazed she is still there."
Mrs May has said she will step down if her Withdrawal Agreement is ratified, but - with the deadline for Brexit extended to the end of October - has not made clear how long she intends to stay if no deal is reached.
Sir Geoffrey Clifton-Brown, treasurer of the 1922 Committee, put the spotlight on a departure date by insisting Mrs May announce a "road map" for her resignation after the European elections set for May 23.
The resumption of government talks with Labour comes amid increased tension between the two sides.
Shadow chancellor John McDonnell said he had no trust in Mrs May after reports emerged that she is ready to offer a temporary customs arrangement with the EU to the opposition.
Labour accused Mrs May of having "blown the confidentiality" of the talks.
Party leader Jeremy Corbyn said Brexit had a big impact on last week's local election results, which saw huge losses for the Tories and a disappointing showing for Labour.
A number of senior Tory Brexiteers have said they would not vote for a customs union.
Referring to talks with Labour, children's minister Nadhim Zahawi said: "Currently, if you look at the Withdrawal Agreement, the customs arrangements, or the alignment with the EU, would go on until December 2021, if Labour believe, actually, that they would rather go to the next general election, which is 2022, for example, then, actually, that's still a temporary customs arrangement.
"And then, whoever is leader of the Conservative Party can then lay out their stall as to the next instalment of negotiations."