Liz Truss’s position as prime minister seems “untenable”, a senior backbench Conservative MP has said.
Miriam Cates, an executive member of the influential 1922 committee, said Ms Truss’s “position does look difficult if not impossible”.
More than a dozen Tory MPs have openly called for Ms Truss to resign after another chaotic day as leader.
Sir Graham Brady, who chairs the 1922 committee, is currently meeting the prime minister.
The 1922 committee sets rules on how the Conservative party elects its leader, and establishes whether the prime minister has the confidence of the party.
A Downing Street source said the prime minister called the meeting with Sir Graham “to keep in touch with the mood of the party”.
Speaking to BBC Radio 4’s World at One programme, Ms Cates said: “I think it seems as though her position is untenable now.
“Let’s see what today holds, but from my point of view it does seem like the confidence of MPs has been lost. I don’t know how that would come back really.”
Earlier, Transport Secretary Anne-Marie Trevelyan said the cabinet still has confidence in Ms Truss.
Under current rules Ms Truss can not be officially challenged in the first 12 months of her premiership – though the 1922 committee executive body could change this.
Ms Cates said: “I do think a leadership contest now would be very disruptive, and it would make it very difficult to make the decisions that we need to make about the economy.”
Her attempts to reassert her authority were torpedoed by the resignation of the home secretary and farcical scenes after a Commons vote on Wednesday.
There is also speculation that senior figures in the party could agree on a replacement for Ms Truss, which would avoid the need for another Tory leadership contest, or a general election.
But the different factions in the party are split over who should take on the job.
So far 13 Conservative MPs have publicly called for the prime minister to resign.
Prime ministers do meet 1922 committee chairs quite regularly. What is different about this meeting is the climate it is happening in.
Sir Graham Brady will know and understand the mood among Tory MPs, so the fact he is going in to speak to Liz Truss is notable.
The fact that the PM has allegedly requested the meeting could mean that she wants to understand the mood of the party or that she had a message she had to deliver to him – we have to be careful with speculation.
But a fractious mood has existed in the Tory party since the mini-budget was announced and it has accelerated in the past 24 hours.
Where all this ends is the question.
Under questioning on the Today programme, Ms Trevelyan declined to say whether Liz Truss will lead the Conservatives into the next election.
“I want her to continue delivering the really important work we’re doing,” she said.
Ms Truss appears determined to fight on – and is attempting to reassert her authority after another day of turmoil, which began when she suspended a senior aid, Jason Stein, who is being investigated for leaking information to the media.
Suella Braverman then resigned as home secretary over data leaks and disagreements over immigration policy. Ms Braverman launched an attack on Ms Truss’s leadership in her resignation letter.
The PM appointed Grant Shapps, one of her harshest internal critics, who she had sacked six weeks earlier as transport secretary, as Ms Braverman’s replacement.
A Labour attempt to get a new law through Parliament banning fracking sparked havoc in the Tory ranks.
MPs were threatened with expulsion from the party if they did not back the government, despite many of them being vehemently opposed to fracking.
Just before they were about to vote, climate minister Graham Stuart told them it would not be treated as a confidence vote in Ms Truss, which some took to mean they could back the Labour motion without fear of being sacked.
This led to chaotic scenes as MPs, who wanted to vote in favour of a ban on fracking, were confronted by cabinet ministers ordering to them to vote with the government.
The speaker of the House of Commons has launched an investigation into allegations of bullying and manhandling of MPs in the voting lobbies by Conservative ministers.
For several hours, it was not clear whether the government chief whip Wendy Morton – the woman in charge ensuring MPs vote the way they are told – had resigned or not.
Overnight, the government issued a statement saying Ms Morton remains in her job – and the fracking vote had always been a confidence vote in the PM.
The Tory MPs who voted in favour of Labour’s fracking ban motion, which the government defeated, would face “proportionate disciplinary action”, the government said.
The prime minister “acknowledges that yesterday was a difficult day” the PM’s spokesperson said, adding: “She recognises that the public want to see the government delivering on policies.”
After the chaotic scenes on Wednesday night, Conservative MP Sir Charles Walker said he was “furious” with the “shambles” – and there was “no coming back” for the government.
Later he added: “I expect the prime minister to resign very soon because she’s not up to her job.”
Some Conservative MPs said Sir Charles was speaking for all of them.