Liz Truss has met with the chair of the 1922 Committee of backbench Conservatives Sir Graham Brady, Downing Street has said.
Downing Street sources said the Prime Minister invited Brady, the powerful chairman of Committee of backbenchers, to No 10 in what appeared to be a hastily-arranged meeting on Thursday.
The MP entered No 10 after the number of Tory MPs demanding the Prime Minister's resignation doubled within just a couple of hours to a dozen after chaotic scenes in the Commons that followed the resignation of Suella Braverman as home secretary.
Truss acknowledged a "difficult day" in her premiership but wants to push on as Prime Minister, her official spokesman said.
It comes as six Tories - Sir Gary Streeter, Sheryll Murray, Miriam Catets, Steve Double, Henry Smith and Matthew Offord - add their voices to calls for the Prime Minister to step down.
They joined Crispin Blunt, who became the first Tory MP to publicly call for Truss to resign on October 16, and five others who had already made their declarations before the chaotic scenes in the Commons on Wednesday night.
Transport Secretary Anne-Marie Trevelyan said the Government is seeking to provide stability and Chancellor Jeremy Hunt should be given the time to set out his financial plans at the end of October.
But a senior MP said Truss has just hours to turn the situation around following the chaos in Parliament on Wednesday.
Trevelyan said she believes "at the moment" it is "still the case" that Truss will fight the next election as Prime Minister.
On Times Radio, Trevelyan said: "I'm looking forward to Jeremy Hunt delivering his statement at the end of the month, and to help us all to be able to get on with delivering our departmental budgets."
But senior backbencher Simon Hoare, chairman of the Commons Northern Ireland Committee, was unable to say whether the country has a functioning Government.
"I think it has a Government that wants to function," he told BBC Radio 4's Today programme, but it is engaged in daily "hand-to-hand fighting".
Asked if Truss is "up to the job", he said: "I think she could be. I think it's... one can't say hand on heart today that there is a... if this was a career review, an employer sitting in front of a person looking at performance and outcomes etc, then the score sheet isn't looking very good.
"But I'm a glass-half-full sort of person. Can the ship be turned around? Yes. But I think there's about 12 hours to do it.
"I think today and tomorrow are crunch days."
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