Foreign Secretary Jeremy Hunt has urged his party to get behind Theresa May as she tries to secure a Brexit departure deal with EU leaders.
The Prime Minister is considering an extension of several months to the UK’s transition period to overcome the Irish border problem.
Her gambit provoked anger among Brexiteers in her own party over the prospect of the UK being bound by EU rules for longer.
But Mr Hunt said Conservatives should follow the example of the 27 EU nations and remain united to allow Mrs May to “maximise her negotiating leverage in Brussels.”
He told BBC Radio 4’s Today programme: “We now need to do the same behind Theresa May to maximise her negotiating leverage in Brussels.”
Other senior Conservatives disagreed, with Scottish Secretary David Mundell fearing that it would tie the UK to the EU Common Fisheries Policy past 2020.
Former Tory leader Iain Duncan Smith warned any extension would cost the UK billions more in EU contributions.
He told BBC Newsnight that the negotiations currently looked “like a capitulation” and that the UK would get nothing in return for an extension.
Mr Duncan Smith added it would be “very hard” to tell the British people that the implementation phase was being extended by another year or more.
“We’re then going to pay tens of billions of pounds over, when we actually say we need it for other domestic programmes,” he said.
Mr Hunt insisted that Mrs May had not capitulated to the EU’s because if she had done so a deal would already have been struck.
Mrs May has proposed the extension to try and avoid a hard border between Northern Ireland and the Republic
The UK is due to leave in March 29 next year, but talks have been deadlocked by the backstop.
Its aim is to avoid the reinstatement of customs checks in the interim between the transition period and any future permanent relationship taking effect.