And Mr Rees-Mogg warned that MPs would not vote for a Brexit deal which failed to meet Mrs May's stated red lines of leaving the single market, customs union and jurisdiction of the European courts.
May will gather her fractious Conservative Cabinet on Friday to try to hammer out a plan for customs and trade ties.
In a podcast for the ConservativeHome website, he said there had been a "breakdown in collective responsibility" in the Cabinet, with pro-EU ministers openly promoting solutions "against the Prime Minister's speeches, against the position formally of the Cabinet and against the manifesto".
So far, May's advisers have come up with two options, neither of which have the full support of her party.
Mr Gove said he is convinced the cabinet "will agree a united position", adding: "Everyone in cabinet is an advocate for Brexit, that is government policy".
Some members of the United Kingdom government have downplayed the corporate warnings.
In a column for the Daily Telegraph he wrote: "Theresa May must stand firm for what she herself has promised".
"This left the Conservatives out of office for 28 years".
"I have great confidence in the prime minister".
It comes after three ministers accused Rees-Mogg of "insolence" and told him to "pipe down" after making another veiled threat against the Prime Minister over Brexit. Responding to May's statement, Jeremy Corbyn, leader of the opposition Labour Party, told the parliament that Conservative division was having a "debilitating effect on this country and threatens jobs and communities".
Brexiteers oppose the PM's favoured option of a customs partnership with the EU, which would see the United Kingdom collect tariffs set by the EU customs union on goods entering the country on behalf of the bloc.
Their "max fac" alternative would, rather than scrapping customs checks, use technology to minimise the need for them.
Both options have been dismissed by the EU.
On Monday, May called on European Union leaders to show flexibility and look "seriously" at the UK's Brexit plans.
Addressing MPs in the Commons on Monday afternoon, May again stressed the United Kingdom would leave the single market and customs union.
However, Remain-supporting MPs argue a pragmatic course is required to avoid disruption for businesses and problems at ports and the border between Northern Ireland the Republic - an European Union member.