Theresa May is to meet the chairman of an influential committee of backbench Tory MPs, Sir Graham Brady, amid calls for her to set a firm resignation date.
No 10 insists the meeting is routine, but pressure is mounting on the PM, with local Tory associations confirming they will hold a vote of confidence in her leadership on 15 June.
Meanwhile, cross-party talks to break the Brexit deadlock are due to resume.
In March, Mrs May pledged to stand down if and when Parliament ratified her Brexit withdrawal agreement with the EU – but she has not made it clear how long she intends to stay if no deal is reached.
The UK had been due to leave the EU on 29 March, but the deadline was pushed back to 31 October after Parliament was unable to agree a way forward.
On Monday, Sir Geoffrey Clifton-Brown, treasurer of the 1922 Committee – an elected body of MPs which represents backbenchers and also oversees leadership contests – told the BBC that Mrs May should announce a “road map” for her resignation after the European elections set for 23 May.
Leading Eurosceptic Sir Bill Cash also told the Press Association “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,” he said.
“The prime minister has already been clear and straightforward that she will see through this first phase of Brexit,” he told BBC Breakfast.
And senior Tory backbencher Sir Oliver Letwin said he believed the PM would remain “in situ” until any Brexit agreement was finally approved by MPs.
Mrs May, who will chair a cabinet meeting later, survived a vote of confidence of her MPs at the end of last year. Under party rules, another vote cannot be held until December 2019.
But pressure is ramping up on Mrs May following last week’s local election drubbing, in which the Conservatives lost 1,334 councillors in England.
In an unprecedented move, the National Conservative Convention – the most senior body within the voluntary party – is to hold a vote of confidence in her leadership next month.
The vote was triggered after 65 local Conservative associations said they had lost trust in the prime minister.
Although the result would not be binding on Mrs May, it would be politically damaging for her to lose the support of grassroots Conservatives.
The prime minister has blamed the Brexit impasse for her party’s terrible performance last week and urged Labour, which failed to make expected gains in the polls and instead lost 82 seats, to compromise to agree a deal.
However, tensions remain as talks between the government and Labour resume.
Labour’s shadow chancellor John McDonnell has said he does not trust the prime minister – after details from cross-party talks were leaked to the press – and accused her of having “blown the confidentiality” of the talks.