Ken Clarke and Harriet Harman are both open to being leaders of a temporary unity government, Liberal Democrat leader Jo Swinson has said.
The party leader said she had spoken to the pair, who have both held their Commons positions for the longest out of all MPs, and won their assurances they are ready to “put public duty first” to “stop us driving off that cliff”.
Swinson said the Labour leader's idea to become caretaker PM was "nonsense" and that there was "no way" he could unite MPs.
In his first comment on the plan mooted by Mr Corbyn, Boris Johnson simply tweeted: "The referendum result must be respected. We will leave the EU on 31st October. #LeaveOct31"
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The Labour leader had written to party leaders and senior MPs asking them to support him in a vote of no confidence which may allow him to become caretaker PM and extend Article 50, with a view to stop no deal.
On Friday, the Mr Corbyn hit back at plans to oust him from guiding a new Government, stating he is "disappointed" in Jo Swinson's response.
He reiterated his party's stance on forwarding a motion of no-confidence in the government to prompt a General Election.
Asked if he would back Ken Clarke or Harriet Harman as a new interim leader, Mr Corbyn said: "We are putting forward the Labour position and I am the leader of the Labour Party do just that."
SNP leader Nicola Sturgeon told Ms Swinson that she should rethink her rejection of the proposition because "we should be prepared to explore all options" to block no deal.
She said: "I think Jo Swinson has got it wrong on this, if she is as serious as I believe she is about wanting to stop a no deal Brexit...then ruling this out at this stage when there is so little time left and so much at stake I think is a mistake."
Ms Sturgeon signalled her 35 MPs could support Mr Corbyn’s plan for a no-confidence vote, extension to the Brexit deadline and general election with him as temporary PM.
Plaid Cymru also suggested it could support the Labour proposal, while some Tory rebels apparently suggested they would meet with Mr Corbyn.
But senior Tory Remainer Dame Caroline Spelman and the Independent Group for Change refused to support any Corbyn government.
The SNP leader told the BBC: “It’s no secret, I’m not the greatest fan of Jeremy Corbyn, but we won’t rule out any option if it helps avert what is a looming catastrophe of a no-deal Brexit.”
Mr Corbyn proposed forming a government on a “strictly time-limited” basis to prevent a sudden departure under Prime Minister Johnson, hoping he could win over his personal critics to support the anti-no-deal cause.
Independent Group for Change leader Anna Soubry said Mr Corbyn “is not the person given he struggles to maintain the confidence of his own backbenchers”.
Dame Caroline also said she could not support the proposal, nor a vote of no confidence in her own Government.
“I could not support a Corbyn Government, end of,” she told the Birmingham Mail.
Green MP Caroline Lewis also called on Ms Swinson to rethink in a “personal appeal”, saying: “Please join us in engaging with Corbyn to see if we can find a way forward.”
Meanwhile, the Greens co-leader Siân Berry told ITV News her party would support a Corbyn led government "if it was seeking a People's Vote" rather than a general election.
On Friday morning, Government Business Minister Kwasi Kwarteng told ITV News: "It was strange that Corbyn is suggesting he should be the leader of the National Government of Unity."
He continued: "He is the most unpopular Leader of the Opposition we have ever had. His poll ratings are disastrous and for him to be saying or posing as a leader who is going to consiliate and unite people I think is ridiculous.
Mr Kwarteng then went on to say Mr Corbyn has "huge" problems within the Labour Party.
Hitting back at Tory colleagues who have expressed support for Mr Corbyn as a leader, the Business Minister said: "Why a Conservative MP, elected on a Conservative manifesto would want to put Corbyn in Number 10 is beyond me."
Former Conservative Sarah Wollaston, who on Thursday became the Lib Dem's latest MP, explained to ITV News why her new boss Ms Swinson had rejected Mr Corbyn as caretaker leader.
She said: "'If you ask any Conservative whether they would vote no confidence in the government in order to support Jeremy Corbyn, they'll tell you they wouldn't.
"So, as I say, it's not about trying to be obstructive, it's about recognising the reality of the situation and also, she's not saying 'look it should be me', she's clearly not saying that, she's saying it shouldn't be any of the party leaders.
"It should be a third party who's widely respected."
Mr Corbyn announced his plan in a letter on Wednesday to opposition leaders and Tory MPs Dominic Grieve, Sir Oliver Letwin and Dame Caroline.
Remain-backing Tory MP Dominic Grieve appeared to agree with Lib Dem leader Swinson, saying "a government of national unity doesn't have to have a leader of any political party as its head".
However the former attorney general did say he and colleagues were "entirely serious" about talking to Mr Corbyn.
He told ITV News: "If we wants to talk to us about stopping a no-deal Brexit, I'm perfectly prepared to speak to him, as are my colleagues."
Although he added: "Putting in a caretaker prime minister must be for some useful purpose. My impression from the letter he's written to me is that he wishes to be a caretaker prime minister to trigger an election.
"The difficulty is that an election in itself doesn't help solve the crisis in relation to Brexit. After an election we may still be in exactly the same crisis so I'm not sure that that's necessarily the best way forward."
Transport Secretary Grant Shapps said: "I think it's absolutely extraordinary that any Conservative MP considered even for one minute installing Jeremy Corbyn in Downing Street.
"Jeremy Corbyn would wreck our economy, he would destroy jobs and the livelihoods, savings, I think he also can't be trusted with security or crime and ... I just think that any Conservative should think very, very hard about doing this. It actually presents a very clear choice.
"You either have Jeremy Corbyn as prime minister overturning the result of the referendum or Boris Johnson respecting the referendum, putting more money into the NHS, more police on the streets to keep us all safe."
Labour frontbencher Angela Rayner responded to Ms Swinson's remarks, saying she "does not get to choose who the leader of the Labour Party is".
Ms Rayner said: "Our leader is Jeremy Corbyn and she should respect the party and respect his title as the official leader of the opposition."
She added: "We are the biggest opposition party, she should work with Jeremy Corbyn - this is party political game scoring."
And Labour MP Tulip Siddiq criticised the Lib Dem's apparent reluctance to work with Labour, writing on Twitter: "The Liberal Democrats were willing to get into bed with the Conservatives for five years, but won’t join with Labour to prevent No Deal?! Are they for real?"
Nick Boles, the independent MP who quit the Conservatives over Brexit and who also received the appeal, has not yet responded.
The Labour leader said he would seek a no-confidence motion soon after the House returns from its summer recess on September 3.
This would need the support of the majority of MPs.
He would then seek an extension to the Article 50 process to delay the UK leaving the European Union past the October 31 deadline.
Then, as PM, he could table a motion for an early general election which would succeed with the support of two-thirds of the seats in the Commons, in the same fashion as Theresa May’s vote in 2017.
Mr Corbyn said Labour would campaign in that election for a second referendum on EU membership with the option to Remain being available to voters.