Rishi Sunak faces the threat of a fresh Conservative rebellion as he sets off on a weekend of frantic diplomacy in an attempt to break the post-Brexit deadlock in Northern Ireland.

With some in his party fearing an intervention by Boris Johnson, the prime minister has been warned his proposed deal on the Northern Ireland protocol does not go far enough after talks with unionists in a Belfast hotel on Friday.

He was also accused of sending mixed messages during a string of discussions with Stormont leaders, intended to mollify their concerns before he flies out to meet EU leaders in Munich.

Jeffrey Donaldson, the leader of the Democratic Unionist party (DUP), said Sunak’s proposal “currently falls short of what would be acceptable” to the party – and failed to adhere to its longstanding red lines.David Jones, the deputy chair of the European Research Group (ERG) of Eurosceptic Conservative MPs, said he was waiting for details before deciding “whether or not whatever deal is proposed is acceptable, not only to the people of Northern Ireland, but the people of the UK as a whole”.

The ERG has said it will remain in “lockstep” with the DUP, and has maintained its demands to remove any jurisdiction from Brussels from Northern Ireland.

Hardline Brexiters in the Conservative party are suspicious of concessions made by the UK, and accused the prime minister of being engaged in a “rolling the pitch exercise, rather than substantive discussion”.

Donaldson refused to criticise any particulars of the agreement and maintained a conciliatory tone while saying the meeting – which overran from 15 minutes to more than an hour – led to “progress”.

He added: “The decisions that will be taken by the prime minister and by the European Commission will either consign Northern Ireland to more division or they will clear a path towards healing and to the restoration of the political institutions.”

Donaldson hinted he would not rush to accept a deal on Sunak’s timetable. “I want to hear that Brussels will stretch itself to recognise the concerns of unionists. This is a process to correct the wrongs of the last negotiation. No one should be led by a calendar. Getting it right must be the goal,” he said.

But Sunak was pressed to move swiftly to resolve the row over the protocol, which has left Northern Ireland without an executive and businesses in limbo.

Leo Varadkar, the Irish taoiseach, said: “When windows of opportunity disappear, sometimes they don’t reappear for quite some time. So I really hope that everyone in Ireland and Europe, in Britain and in Northern Ireland will seize this opportunity if it arises.”

The UK prime minister is preparing to meet Ursula von der Leyen, the European Commission president, on the sidelines of the Munich Security Conference on Saturday lunchtime, where the pair are likely to discuss the final contours of an agreement to replace the current trading arrangements. He is also likely to meet the leaders of France and Germany.The UK foreign secretary, James Cleverly, said his meeting with Brussels’ chief negotiator, Maroš Šefčovič, and diplomats from the EU27 was “constructive” and that “intensive work continues”.

“We are in sight of the harbour, but we are not quite there yet,” one EU diplomat said, noting that Šefčovič had detected a turning point in British attitudes since Sunak entered No 10. “The tone was fundamentally different from what we have seen over the past eight years … [Sunak] is more interested in finding actual solutions than posturing and solutions that are just solutions in name only.”Late on Friday, Sunak said “there is more work to do” on finding a deal “protect the Belfast Good Friday agreement and Northern Ireland’s place in our single market”. He added: “Now it is clear that we need to find solutions to the practical problems that the protocol is causing families and businesses in Northern Ireland, as well as address the democratic deficit.”

Though No 10 sought to play down suggestions a deal had already been reached, expectations in Brussels and Westminster are that Sunak is pushing to secure one by Tuesday.

A vote in parliament could be held that day on a command paper containing the changes, with the prime minister facing the embarrassing prospect of a Tory rebellion if any checks on goods between Great Britain and Northern Ireland – and the role of the European court of justice as an arbiter – remain.

Party whips admitted they were unprepared for a vote, with no higher level of engagement with backbenchers planned for the weekend. Instead, the Vote Leave strategist Oliver Lewis was said to have been dispatched to court potential rebels. Labour is expected to back any deal agreed between the UK and the EU.

They fear that a critical pronouncement by Johnson, who negotiated the protocol as part of his Brexit deal, could risk swaying enough MPs to slash the government’s majority in the Commons.But Sunak was accused of sending mixed messages back home by party leaders in Belfast. Some admitted they thought a breakthrough was just days away, while others suggested it could it be weeks.

There were signs that the DUP was sceptical its seven tests for supporting any new deal to change the protocol had been met – the key condition for re-establishing an executive at Stormont, which has been dormant for a year.

The EU is understood to have conceded ground on the issue of customs checks on goods moving from Great Britain to Northern Ireland. The UK had proposed a system of red and green lanes for lorries that would allow goods in the latter category to avoid customs declarations.

EU officials believe a compromise with lighter checks is possible because the UK has agreed to share real-time customs data to track the movement of goods.

The role of the European court of justice in policing the Northern Ireland agreement will remain, but there will be more layers of arbitration before disputes are referred to Luxembourg. Currently, the first port of call for disputes is a UK-EU “specialised committee”, but there will be additional venues for airing disputes about the protocol before going to the European court.

While EU sources expect Sunak to announce a deal on Tuesday, they remain unsure whether he can sell it to his Eurosceptic backbenchers and the DUP. “With the UK, you never know,” said an official. “We should hope [there is a deal] because I don’t see anyone else who is capable of doing it.”