Tory Brexiteers and ministers have been urged to give Rishi Sunak the “time and space” to “thrash out” a new deal on the Northern Ireland Protocol amid fears of a rebellion.

The Prime Minister faces a challenge in his own party as Britain and the European Union inch closer to an agreement seeking to resolve tensions over post-Brexit arrangements.

Fresh high-level talks with Brussels were arranged as Mr Sunak met with his Cabinet as he seeks to satisfy the demands of Northern Ireland’s Democratic Unionist Party (DUP).

He is facing calls to allow MPs a vote on any final deal and the Times reported that some ministers could resign if his solution risks Northern Ireland’s position in the UK.

Health minister Maria Caulfield told Times Radio: “I think we need to support the Prime Minister.

“There isn’t a deal done yet so all these rumours about ministers or MPs not being happy, I haven’t seen the details, we have to give the Prime Minister that time and space to get these negotiations done.

“We need to give him the time and space to thrash out the final elements of any final deal.”

But prominent Eurosceptic Jacob Rees-Mogg criticised Mr Sunak’s tactics, comparing him to doomed predecessor Theresa May.

He said Mr Sunak should press ahead with the Northern Ireland Protocol Bill, effectively ripping up parts of the agreement with Brussels, rather than seeking a deal which may not guarantee the return of a powersharing executive in Stormont.

On his ConservativeHome podcast, Mr Rees-Mogg said: “There seems to me to be no point in agreeing a deal that does not restore powersharing.

“That must be the objective. If it doesn’t achieve that objective, I don’t understand why the Government is spending political capital on something that won’t ultimately succeed.”

He said the Northern Ireland Protocol Bill had the support of “the person who had a mandate from the British voters” – Boris Johnson – and he questioned Mr Sunak’s handling of the situation.

“I don’t know why so much political capital has been spent on something without getting the DUP and the ERG (European Research Group of Conservative MPs) onside first,” he said.

It was “very similar to what happened with Theresa May” where a policy would be presented in the hope that people would “conveniently fall in behind” it, he said.

“Life doesn’t work like that. It’s important to get support for it first before you finalise the details and that doesn’t seem to have been done here.”

Foreign Secretary James Cleverly and Northern Ireland Secretary Chris Heaton-Harris were to hold fresh video talks with European Commission vice-president Maros Sefcovic on Tuesday afternoon.

They held “productive” talks on Monday and the EU said they still plan to meet for scheduled face-to-face talks later this week.

Mr Johnson has called on the Government to press on with the legislation enabling it to override parts of the protocol and some have interpreted words from Home Secretary Suella Braverman as support for the former prime minister’s position.

She described the Northern Ireland Protocol Bill as “one of the biggest tools that we have in solving the problem on the Irish Sea”.

Ms Braverman, a longstanding Eurosceptic, argued that Mr Sunak is right to be “committed to finding a pragmatic solution to resolve these issues”.

Ms Caulfield said: “I think what Suella has actually said is she welcomes the Prime Minister’s negotiations on this both with the EU and with politicians in Northern Ireland to try and get this resolved.

“Absolutely the Northern Ireland Protocol Bill was put in place as a mechanism to fall back on and that’s still going through Parliament at the moment.”

There are hopes a deal on the protocol that is acceptable to unionists could secure the return of powersharing at the Stormont Assembly, after the DUP walked out in protest over post-Brexit arrangements last February.

Focus has also turned to the fate of the Northern Ireland Protocol Bill, which is currently stalled in the Lords and would allow ministers to override parts of the protocol.

The intervention by Mr Johnson, who negotiated the protocol but whose Government also tabled the Bill at Westminster after unionist outcry, was a sign that some backbenchers may try to scupper any agreement brokered by Mr Sunak if it fails to address longstanding concerns about the settlement in Northern Ireland.

The ERG, a band of Eurosceptic Conservative MPs, is expected to meet for talks later on Tuesday.

Sir Keir Starmer has urged the Prime Minister to allow the Commons to have its say on any final deal, offering Labour support to secure the approval of any new agreement in the event of any Tory rebellion.

It comes as former Northern Ireland secretary Brandon Lewis threw his weight behind calls to reform some of the post-Good Friday Agreement architecture in Northern Ireland, arguing that it was failing to reflect the changed electoral landscape in the region.

“The growth in the vote for the Alliance Party underlines the feeling that many more people now want to vote on issues, not on sectarian lines,” Mr Lewis wrote in the Telegraph newspaper.

“That should be embraced as the greatest success of the Belfast/Good Friday Agreement. But if the agreement does not evolve further, under current rules, if Alliance and its vote share continues to grow, it will never have the right to nominate the First or Deputy First Minister.

“Democracy cannot succeed when it is set in tram lines that can never cross.”