Michael Gove says he "absolutely" has confidence in Theresa May as she pursues her Brexit deal.
Rumours had been rife that the environment secretary would follow fellow Brexiteers out of the cabinet in protest at the EU withdrawal agreement.
But he told reporters on Friday that he was focused on working in cabinet to get "the right deal in the future".
Mr Gove reportedly rejected an offer to make him Brexit secretary after Dominic Raab's exit.
The PM has said her Brexit agreement is "truly the best deal for Britain".
According to BBC, Mr Gove said he would only accept the job of Brexit Secretary if he could try to make changes to the negotiated deal - something Mrs May and EU leaders have made clear is not possible.
Asked if he had confidence in the PM, Mr Gove said: "I absolutely do."
He added: "I'm also looking forward to continuing to work with all my government colleagues and all my colleagues in parliament in order to make sure that we get the best future for Britain.
"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 the right outcome."
Fellow Brexiteer and cabinet member Liam Fox told an event in Bristol: "We are not elected to do what we want to do, but to do what is in the national interest."
Speaking in public for the first time since the withdrawal agreement was signed off by cabinet, he said he hopes MPs "will take a rational and reasonable view" of the deal.
He added: "I hope across parliament we recognise that a deal is better than no deal, and businesses require certainty - it's in our national interest to provide certainty as soon as possible."