The DUP has poured cold water over a reported Brexit compromise to end the deadlock over the backstop.
Deputy leader Nigel Dodds warned the mooted plan - reportedly being discussed by EU and UK officials in Brussels - "cannot work".
Reports from the Belgian capital claimed British Prime Minister Boris Johnson has sought to revive a proposal first put forward by former prime minister Theresa May for a customs partnership between the UK and the EU.
The scheme, intended to avoid the need for customs controls on the island of Ireland, would see Northern Ireland remain politically in a customs union with the EU but it would be administered by the UK.
However Mr Dodds - whose party's votes will almost certainly be needed to get a Brexit deal through parliament - told the Italian La Repubblica newspaper that Northern Ireland "must stay in a full UK customs union, full stop".
"It cannot work because Northern Ireland has to remain fully part of the UK customs union," he said.
He added: "There is a lot of stuff coming from Brussels, pushed by the Europeans in the last hours, but one thing is sure: Northern Ireland must remain fully part of the UK customs union. And Boris Johnson knows it very well."
British officials have so far remained tight-lipped in the face of the reports.
The reported plan would create a customs border in the Irish Sea with goods travelling from the rest of the UK to Northern Ireland being subject to tariffs which Britain would collect on behalf of the EU.
Businesses would then be able to claim a rebate once they had shown the goods were for consumption in the UK market.
However it would mean that Northern Ireland would be able to benefit from any post-Brexit trade deals the UK struck with other countries around the world.
Speaking during a school visit yesterday, Mr Johnson repeatedly refused to say whether he had offered any concessions on the issue of the customs union.
He stressed however that he would not accept anything that "damages the ability of the whole of the United Kingdom to take full advantage of Brexit".
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Meanwhile, DUP leader Arlene Foster warned they would only back measures that were in the "long-term economic and constitutional interests " of Northern Ireland.
Ms Foster said: "In order to secure a sensible deal for everyone it is important that the European Union understand that to maximise the prospects of agreement there will need to be a clear acceptance that the economic and constitutional integrity of the whole of the United Kingdom will have to be respected as we leave.
"As a consequence of the mandate given to us by voters in 2017 (general election) the DUP is very relevant in the parliamentary arithmetic and regardless of the ups and downs of the Brexit discussions that has not changed."
The EU's chief negotiator, Michel Barnier, gave the green light yesterday for intensive discussions between officials to start.
Mr Barnier is due to brief EU ambassadors and MEPs on Monday on progress.