Theresa May will face tough questions later from her backbenchers after the Conservatives lost their majority at last week’s election.
The MPs are expected to raise concerns about her leadership style, and press for more details on talks with the Democratic Unionists.
Mrs May’s new cabinet will also meet for the first time after a reshuffle.
Brexit Secretary David Davis predicted some parts of the Tory manifesto would now have to be “pruned”.
“We have been given an instruction by the British people,” he told BBC Radio 4’s Today programme.
Mr Davis said that while the Tory election campaign had been disappointing, Mrs May was a “formidable prime minister” and accused people speculating about her leadership of “the absolute height of self-indulgence”.
The meeting of the 1922 Committee of backbench Tory MPs comes after the PM finalised her cabinet, with Michael Gove returning as environment secretary.
Mr Gove, a former Cabinet minister and leadership rival to Mrs May before she became Conservative leader, was sacked by the PM in her reshuffle in July last year.
The Conservatives lost their House of Commons majority in Thursday’s snap election, going from 331 seats to 318, while Labour increased its number of MPs from 232 to 262.
BBC political correspondent Iain Watson says the meeting with the committee had been brought forward by 24 hours, not because of panic within the party, but possibly as a way of avoiding it.
One MP told him: “The wise heads will need to tell any hotheads to calm down.”
Graham Brady, the leader of the 1922 committee, told BBC One’s Sunday Politics there was “zero appetite” among the public for another election.
Labour leader Jeremy Corbyn has accused Mrs May of “squatting” in No 10, telling the BBC’s Andrew Marr Show on Sunday that the country “cannot go on with a period of great instability”.
A number of high-profile members kept their posts in Sunday’s cabinet reshuffle, with Philip Hammond staying at the Treasury, Boris Johnson remaining at the Foreign Office and Amber Rudd keeping the Home Office brief.
But some changed jobs too, with Liz Truss being demoted from justice secretary to become chief secretary to the Treasury.
Damian Green, who was work and pensions secretary, has been promoted to become the first secretary of state – effectively Mrs May’s second in command.