Home Secretary Amber Rudd has said ministers will not be intimidated by threats of a leadership challenge to Theresa May from Tory Brexiteers.
As the Cabinet's Brexit sub-committee prepares to meet for two days of talks on the UK's future relationship with the EU, Ms Rudd insisted they would come forward with proposals which would command broad support in the party.
Amid warnings from Brexiteers that Mrs May must stand by her commitment to leave the EU customs union as well as the single market, she said ministers were committed to getting a deal which would enable Britain to strike free trade deals with other countries while maintaining "frictionless" trade with the EU.
"I have a surprise for the Brexiteers, which is the committee that meets in order to help make these decisions is more united than they think," she told BBC1's The Andrew Marr Show.
"We meet in the committee. We meet privately for discussions. I think that we will arrive at something which suits us all.
"There will be choices to be made within that, but we all want the same thing which is to arrive at a deal which works for the UK."
Ms Rudd acknowledged that it would probably involve some form of customs "arrangement" or "partnership" with the EU, but said the Prime Minister had an "open mind" as to how that could be achieved.
"We a want frictionless trade at the border, we want to make sure that there is no border on the island of Ireland and we want to make sure that we can do trade deals outside of the European Union. That is the deal we are looking for," she said.
"We need to have this wider agreement. I don't know how far that will go over the next few weeks but I hope the Government will be give the space to try and achieve that."
Her intervention came as the senior Tory backbencher Bernard Jenkin launched a fresh attack on Chancellor Philip Hammond, accusing him of pursing his own policy on Brexit.
The Chancellor caused fury among Brexiteers when he suggested at the World Economic Forum in Davos that Britain's relationship with the EU might only change "very modestly" after leaving.
Writing in The Sunday Telegraph, Mr Jenkin said that it was now time for all ministers to get behind the Prime Minister and support the agreed Government position.
"She can only command a majority in Parliament on her present policy. Nearly half David Cameron's MPs, voted Leave, despite his patronage and pleadings. There would have been few Remain Tories if he had advocated Leave," he wrote.
"Her MPs will back her, because we are overwhelmingly at one with the majority of the British people who now want a clean Brexit and an end to the present uncertainty.
"It is time for all her ministers to back her too and to end the confusion they are fomenting in government."