“Those who have said they will do anything necessary to stop the long-term damage of a no-deal exit must take seriously this type of offer,” Mr Bebb said.
“I certainly take the view that a short-term Jeremy Corbyn government is less damaging than the generational damage that would be caused by a no-deal Brexit.”
Mr Corbyn has called for Boris Johnson to be toppled – when MPs return to Westminster next month – with himself installed as a stopgap premier to block a no-deal exit on 31 October.
Mr Bebb – who is standing down at the next election – added to growing pressure on Jo Swinson, the new Lib Dem leader, to rethink her outright opposition to Mr Corbyn’s audacious bid.
Ms Swinson accused Mr Corbyn of “demanding the keys to No 10 as a precondition for a vote of no confidence”, which Labour signalled would come within “days” of the Commons sitting on 3 September.
“What we need in a leader of an emergency government is a long-serving member of parliament who is respected on both sides of the house,” she said.
“Someone like Ken Clarke or Harriet Harman – the father and mother of the house. They are hugely experienced and, unlike Jeremy Corbyn, or indeed myself, they are not seeking to lead a government in the long term.”
But Caroline Lucas, the Green MP, issued a video message urging Ms Swinson to rethink, saying: “Jo, please change your mind. Jeremy Corbyn has done the right thing.”
Urging the Lib Dem leader to join talks, Ms Lucas added: “Let’s have that negotiation with him and not reject this offer out of hand.”
Nicola Sturgeon, the Scottish National Party leader, echoed the call, saying: “Jeremy Corbyn’s suggestion is not the only possible option – but given the circumstances, nothing should be ruled out at this stage.
“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.”
Senior Tories Dominic Grieve, Caroline Spelman and Sir Oliver Letwin issued a joint letter, with former Conservative Nick Boles, welcoming talks, but did not endorse the Labour leader as a stopgap in No 10.
But Anna Soubry, the leader of the Independent Group for Change, said: “I would not support a government of national unity that is led by Jeremy Corbyn for all manner of reasons.”
Mr Bebb’s endorsement of a Labour prime minister – even a temporary one – is certain to trigger calls for him to be stripped of the Conservative whip.
The StandUp4Brexit campaign of grassroots Tories was furious, saying: “Are MPs like Guto collaborating with the EU in a vain attempt to overturn Brexit, and to hell with the consequences for British democracy?”
Join our new commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies