Thirteen ministers – including eight who voted to remain in the EU – reportedly told The Sunday Times they would back the prime minister's decision in the event negotiations with the EU failed.
"I'd much rather we had a deal but he's got a no-deal mandate if that is his judgement," one minister is said to have told the newspaper, before claiming that the economic impact of Covid is “much bigger” than Brexit.
"Just get it done," another reportedly said. "The PM should do what is best. He has total, 100 per cent rock-solid support".
The apparent show of unity within the government came after the UK and EU agreed to restart negotiations on Sunday in a last-ditch attempt to resolve what were described as "significant differences".
After months of talks, both sides have failed to reach agreement on the three major issues of fishing rights, the "level playing field" relating to state aid and business standards, and the mechanism for resolving future disputes.
In a joint statement, Mr Johnson and the European Commission president Ursula von der Leyen said that no free-trade agreement was "feasible" unless they could bridge the long-standing gaps between their positions.
Meanwhile France's minister for European Affairs denied reports of a split between the 27 EU leaders on the handling of the trade talks.
"The British gamble of a split within the Union failed," Clement Beaune told the Journal de Dimanche. He also reaffirmed that France was willing to veto any deal if it did not get "large and lasting access" to fish quotas in British waters.
However SDLP leader Colum Eastwood, the Irish nationalist MP for Foyle in Northern Ireland, described the latest developments as "lots of theatrics".
He said: "The ongoing talks between Britain and the EU seem very much like the end of every negotiation that ends positively. The bottom line is Britain needs a deal. If they don't do it there'll be huge economic consequences on top of the impact of Covid."
Mr Johnson and Ms von der Leyen are due to hold another phone call on Monday evening – at the same time as the House of Commons reconsiders the sections of the UK Internal Market Bill which envisage breaking international law by rewriting the Brexit deal signed by Boris Johnson last year.