Theresa May will face tough questions later from her backbenchers after the Conservatives lost their majority at last week’s election.
The 1922 committee is also expected to raise concerns about her leadership style, and press for more details on talks with the Democratic Unionists.
Mrs May hopes to strike a deal with the DUP to support her minority government.
The meeting comes after she 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 has been brought forward by 24 hours.
This was not because of panic within the party, but possibly as a way of suppressing it, he adds.
‘Wise heads v hotheads’
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.
Analysis by BBC political correspondent Iain Watson
Widespread demands for Mrs May to go are not expected at Monday’s 1922 committee meeting.
Instead, there will be demands for her to consult more, including meeting regularly with the 1922 executive, and to turn Downing Street from a bunker into an open house by broadening her range of staff.
However, few MPs expect her position to be strong and stable for the next five years.
One senior backbencher told me: “It is inconceivable she will lead the party into the next election. Her authority has been diminished unquestionably.”
Another said: “Party members have been too bruised by her.”
“She has bought herself some time”, said another senior backbencher, but added: “How she behaves will determine how long she’s there.”
There is a feeling that the party is holding on to nurse for fear of something worse.
Johnson: MPs should get a grip
After speculation in the Sunday newspapers that he was mounting a leadership challenge, Mr Johnson has called for Tory MPs to back Mrs May.
Writing in Monday’s Sun, the foreign secretary said those calling for the PM to step down should “get a grip”, adding the electorate wanted the government to “get on with the job”.
Mr Johnson admitted the prime minister’s election campaign did not go well – “to put it mildly” – and that Tory messages “got lost or misunderstood”.
But he added: “Theresa May led a campaign that inspired 13.7m people to vote Conservative, in the biggest total tally of Tory votes since the days of Margaret Thatcher.
“That is a stunning achievement, for which she deserves the support of her party. And she will certainly get it from me.”
He also said the proposal of a deal with the DUP to keep her minority government in power was “feasible”.
“The people of Britain have had a bellyful of promises and politicking,” he wrote.
“Now is the time for delivery – and Theresa May is the right person to continue that vital work.”
The return of Mr Gove to the front bench as environment secretary has been a shock to some, including the politician himself.
Speaking to Sky News on Sunday, he said he had been “quite surprised” to be asked to rejoin the cabinet.
He added: “Of course I knew that today was reshuffle day, but I genuinely didn’t expect this role – although I am delighted to be part of the government, and delighted to be able to support Theresa.”
However, the BBC’s environment analyst Roger Harrabin says green campaigners are appalled at Mr Gove’s appointment because of his links to the climate sceptic wing of the Conservatives.
They point to his time as education secretary, when he tried to remove climate change from the geography curriculum, and as chief whip, when he blocked the then environment secretary from important international talks.
Tom Burke, from green think tank E3G, told BBC News: “The environment is something young voters really care about.
“If the Tories really want to reconnect with the youth surge, this is about the worst option they could have chosen.”
But others have welcomed the new minister.
One senior farming industry source said they were happy that a “big hitter” was taking the top job at the Department for Environment and Rural Affairs (Defra).
“Defra has long been a backwater, so at last it’s not someone in charge who is being put out to grass,” he said.