Senior Tory MP Sir Oliver Letwin has said he does not support Jeremy Corbyn becoming a caretaker prime minister in a bid to avoid a no-deal Brexit.
But he backed discussions across the Commons to prevent the UK crashing out of the EU without a deal.
Prime Minister Boris Johnson has pledged that the UK will leave the EU by 31 October “do or die”.
Mr Corbyn said the UK needs a government that is “prepared to negotiate” with the EU.
His current plan is to win a no-confidence vote in the government, become interim prime minister and “do everything we can” to stop a no-deal Brexit.
Once in the role of caretaker prime minister, Mr Corbyn say he intends to delay Brexit, call a snap election, and campaign for another referendum.
Sir Oliver, who was among senior Tories who received a letter from Mr Corbyn about the plan, was asked about Mr Corbyn’s proposal on BBC Radio 4’s Today programme.
“That appears to be his agenda. I have to say it is not one I personally share,” he said.
“I don’t think it’s at all likely that a majority would be formed for that and I personally wouldn’t want to vote for it. I wouldn’t be able to support that, no.”
Sir Oliver, a former cabinet minister, has led several attempts in Parliament to break the Brexit impasse and prevent a no-deal Brexit.
But he said he was “not very inclined” to help bring down the government in a no-confidence vote and would “rule it out” if it led to Jeremy Corbyn becoming prime minister.
His comments came amid an ongoing row among MPs who oppose no deal, with Liberal Democrat leader Jo Swinson initially dismissing Mr Corbyn’s plan as a “nonsense”.
Mr Corbyn said he assumed everyone who wanted to avoid a no-deal Brexit – including the Liberal Democrats – would vote for the motion of no confidence that Labour intends to launch against the government.
“What we need is a government that is prepared to negotiate with the European Union so we don’t have a crash-out on the 31st,” he added.
Anna Soubry, leader of the Independent Group, said she would “not support nor facilitate any government led by Jeremy Corbyn”.
But the head of the SNP, Nicola Sturgeon, was among those applying pressure to Ms Swinson to change her stance.
The Liberal Democrat leader suggested Tory grandee Ken Clarke or former Labour deputy leader Harriet Harman could head a temporary government instead of Mr Corbyn.
Mr Clarke responded on Friday to say he was willing to lead a government of national unity to avoid a no-deal Brexit.
Asked if Mr Clarke or Ms Harman could lead the country through a political crisis, Mr Corbyn said: “What we need is a respect for the electoral process that brought about the results from the last general election.”
Sir Oliver suggested the majority of MPs did not want a no-deal Brexit, although he said he was “not terribly optimistic” they would reach an agreement.
The former minister, who has agreed to meet with Mr Corbyn to discuss plans to avoid a no deal, said opponents of the government’s Brexit position needed to “talk a lot” and “talk frankly”.
Meanwhile, fellow senior Tory MP Dominic Grieve said there was a “a considerable head of steam growing to try to make sure that no deal doesn’t occur”.
He also refused to back the Labour leader to be a caretaker prime minister, telling BBC Radio Scotland’s Good Morning Scotland programme it was “absolutely vital” any interim PM commanded “high levels of trust”.
“I simply don’t think that Jeremy Corbyn, as leader of the Labour Party – and particularly with his very strong views, which he’s entitled to – is the right person,” he said.
Although he said he himself would be willing to be a caretaker prime minister, he said, “there are others who are rather more suitable for doing it than I am”.
Mr Grieve, a former attorney general, said there was a “growing number” of Tory MPs who were “horrified” by the direction of Mr Johnson’s government.
“His views, and the way he’s expressing them, are so removed from what I would describe as proper and traditional conservatism as to cause real disquiet,” he said.
“We have a deeply divided country and we are not going to resolve this problem by this type of tub-thumping populism. “
He accused the prime minister of “behaving like a demagogue”. He said Mr Johnson’s language had led to members of the public sending death threats to him for his role in trying to prevent a no-deal Brexit.
Mr Johnson earlier this week accused MPs “who think they can block Brexit” of a “terrible collaboration” with the EU.
“If leading politicians use language – collaborator is an obvious one – or call people a traitor, you immediately start to receive really vile emails and communications,” Mr Grieve said.
Tory MP and Brexiteer Sir John Redwood told Today he was not worried about opposition to the government’s Brexit stance.
“I would be surprised if this parliament developed a majority to thwart the British people because the overwhelming majority of MPs were elected on a clear promise to see us out of the European Union with a deal if there’s a good deal on offer and without the deal if there wasn’t a good deal on offer,” he said.