The Justice Secretary faced furious accusations of treachery from Mr Johnson’s allies after his devastating assessment that the former London mayor was incapable of providing the leadership the country needed.
Rival leadership contender Liam Fox said the feuding between the two men was a “distraction” and that the country needed “Brexit for grown ups” in the wake of last week’s referendum vote to leave the EU.
Veteran former chancellor Ken Clarke said the race to succeed David Cameron at No 10 was in danger of being reduced to the level of a farce and he urged Mr Gove to withdraw from the contest.
With a potential financial crisis looming, he said that it was essential for the country to restore stable leadership as quickly as possible.
“I do think Michael Gove would do us all a favour if he were to stand down now and speed up the process,” he told the BBC Radio 4 Today programme.
“One of the first priorities for a leader of a party and certainly for a prime minister is that you should have the trust so far as possible of your colleagues.
“It is not encouraging that he stood alongside Boris throughout the campaign as his right hand man. He was publicly declared to be his manager.
“We don’t want to add to tragedy too much of an air of farce and for him to emerge now as a prime minister saying ‘I’m now going to reunite the party, I now have a clear vision of what I am going to do’ is I think unlikely.
“I just think that this kind of public performance is more suitable to the election of a student union than it is to be prime minister of this country at a time of pretty grave potential crisis.”
Dr Fox, the former defence secretary who campaigned for Leave, said that Mr Gove and Mr Johnson appeared to be preoccupied with the student politics of their Oxford University days.
“We are now 10 weeks away from having a new prime minister, we’re in the process of electing a prime minister who will actually take us out of the European Union, and yet we seem to be permanently distracted by what can only be described as the politics of the Oxford Union in recent days,” he told the Today programme.
“I think it was a distraction, we need Brexit for grown-ups and we need to be talking about the big issues.”
The onslaught came as Mr Gove prepared to formally launch his leadership bid with a speech at Westminster setting out his plans for the premiership.
One of his leading supporters, Justice Minister Dominic Raab, hit back at Mr Clarke, a long-time Remain supporter, of trying “to knock out the strongest Brexit candidate” in the leadership race.
“I do think we need to allow the dust to settle and focus on who has got both the vision and the capability to deliver for this country going forward,” he told the Today programme.
“There’s a lot of raw nerves around, but I can see through the mist that we’ve got a critical choice ahead and I think Michael Gove is the change candidate with the vision, but also the track record, to deliver both on Brexit and the aspirational society we need.”
Mr Johnson’s shock withdrawal from the contest has left Home Secretary Theresa May the clear frontrunner.
She has continued to attract more heavyweight backing with declarations of support from Cabinet colleagues Michael Fallon and Patrick McLoughlin.
The focus now appears to be on the battle for second place, which will decide which of the four other candidates goes forward with her into the final ballot of grassroots party members.
The field of five is completed by Work and Pensions Secretary Stephen Crabb and Energy Minister Andrea Leadsom.
Mrs May is the voters’ favourite to become the next prime minister, according to an Opinium poll which found a quarter of Britons (24%) back the Home Secretary.
But her “reluctant Remainer” position during the referendum may hurt her chances, with 55% believing the next PM needs to be pro-Brexit to get the best deal from the EU, the survey of 2,001 adults showed.