Sir John Major has urged people to re-elect three MPs who were expelled from the Conservatives for voting against Boris Johnson over Brexit.
The ex-Tory PM is backing independent candidates David Gauke, Dominic Grieve and Anne Milton, all running against his party in the general election.
Sir John said "tribal loyalties" had been loosened by Brexit.
But Mr Johnson described the comments as "very sad" and "wrong", calling his predecessor's views "outdated".
The Conservatives say they will take the UK out of the EU in January if they win a parliamentary majority.
They say this honours the result of the 2016 referendum, in which 52% of people backed Leave.
In September, 21 MPs were expelled from the parliamentary Conservative Party after they had voted against the possibility of the prime minister pursuing a no-deal exit from the EU. Later, 10 of the MPs were allowed back.
Of the remainder, Mr Gauke, Mr Grieve and Ms Milton are all running as independents in the seats they held at the 2017 general election.
In a video message, Sir John, a prominent Remain campaigner, described Brexit as "the worst foreign policy decision in my lifetime".
He called Mr Gauke, Mr Grieve and Ms Milton "principled, decent human beings".
He added: "None of them has left the Conservative Party; the Conservative Party has left them.
"Without such talent on its benches, Parliament will be the poorer, which is why - if I were resident in any one of their constituencies - they would have my vote."
In response, Mr Johnson said he disagreed with his "illustrious predecessor".
He added: "I think it's very sad and I think that he is wrong, and I think that he represents a view that is outdated, alas, greatly that I respect him and his record
"And I think that what we need to do now is honour the will of the people and get Brexit done."
Another former prime minister, Labour's Tony Blair, warned that Brexit "won't be over" in January.
He added that it was "undemocratic" to be "mixing up Brexit with a general election" .
Mr Blair also said: "Brexit is the substitute of a comforting delusion for the discomforting challenge of a changing world."
Mr Johnson says a Conservative government would be able to reach a post-Brexit trade deal with the EU by the end of 2020.
Mr Gauke was among those who disputed whether this was possible within the timeline suggested by the prime minister.
But Mr Johnson said the UK was in a "zero-tariff, zero-quota position" already, which would make the talks easier.
Mr Gauke said he was "delighted" to have backing from Sir John, who "represents the best traditions of the Conservative Party".
And Mr Grieve said he had been an "outstanding PM and Conservative whose moderation and common sense put Mr Johnson to shame".
Speaking on a visit in Hampshire, Liberal Democrat leader Jo Swinson said the ex-PM's intervention showed Mr Johnson had taken the Conservative Party "off to the extreme".
"This is a party that bears no resemblance to the One Nation Conservatives that many moderate people in this country have appreciated and that's one of the reasons so many of those people are now going to be voting Liberal Democrat," she said.
Sir John, who was prime minister between 1990 and 1997, is a long-standing critic of the government's Brexit plans.
In September, he joined a lawsuit against the suspension of Parliament by Mr Johnson, arguing it was designed to stop MPs being able to prevent a no-deal Brexit on the then deadline of 31 October.
The Supreme Court declared the suspension unlawful.