Mr Gove also said he had "absolute" confidence in the Prime Minister, while Dr Fox, the International Trade Secretary, said it was "in the national interest" to back her.
Former Brexit minister Steve Baker, a member of Jacob Rees-Mogg's European Research Group, said he had a list of more than 48 MPs who had sent letters, enough to trigger a ballot under the party's rules.
South Staffordshire MP and Defence Secretary Gavin Williamson said: "I'm very supportive of the Prime Minister".
"I know that Gibraltar has no intention of being a back door, but instead a centre of high quality financial services", Mr Barclay said at the time.
In a public relations offensive, May tried to win support in a Daily Mail interview that revealed how her husband supported her during what she admitted to be "a pretty heavy couple of days". "We need to be going out there and grasping opportunities", Raab told the paper.
He has been congratulated on Twitter by Chief Secretary to the Treasury Liz Truss, who said he was "a star" when he worked in her department.
At present, there appears to be no parliamentary majority for the deal, which would have to be voted through before final approval.
A Remain supporter during the 2016 referendum, Ms Rudd has given her backing to Mrs May's draft Brexit agreement, saying it is "not flawless but ideal was never on offer".
The prospect of May's ouster or the deal's failure in the British Parliament has raised concerns that Britain could try to renegotiate the agreement before its scheduled exit on March 29, 2019.
"It is tight and I accept that, and that is the frustration, that we have got right the way across the House of Commons, the frustration of why has the last two years have been wasted in the way it has, in the internal disputes within the Conservative Party, when there should have been these negotiations". However, if push came to shove, there would probably be room for at least some European Union flexibility in order to avoid a damaging no-deal Brexit.
Mrs May agreed a draft withdrawal agreement for Brexit with her cabinet on Wednesday, which had already been signed off by negotiators from both the United Kingdom and EU.
Councillor Samantha Hoy of Wisbech, a prominent Conservative district and county councillor and leader of the town council, said: "I am unhappy with Theresa May's Brexit plan as I don't believe it delivers a true Brexit".
"I think it's absolutely vital that we focus on getting the right deal in the future, and making sure that in the areas that matter so much to the British people we can get a good outcome", he said.
In a sign the Tory civil war over Brexit is not slowing down, Middle East Minister Alistair Burt warned rebels the "consensus" that pro-EU MPs should reluctantly respect the 2016 referendum result could break down if she is toppled.
"The proposition would be: 'So far we've failed, can we have a vote of confidence please?'"
He also said it showed Theresa May's confidence that she could appoint one of her "allies" to such a key role given the turmoil over her leadership in the past 24 hours.