DUP leader Arlene Foster has claimed that the draft EU Brexit text is not "faithful" to the deal reached in December.
The former Stormont first minister said she told EU chief negotiator Michel Barnier during a "constructive" meeting in Brussels on Tuesday that the text on future customs arrangements between the EU and UK was "unacceptable".
She also said she had advised Mr Barnier that he had "overreached" in suggesting Northern Ireland could stay in the customs union after Brexit.
Mrs Foster was speaking following a meeting with Mr Barnier in the European Commission. She was accompanied by party colleagues MP Nigel Dodds, Brexit spokesman Sammy Wilson and MEP Diane Dodds.
"We stressed again the need to respect the constitutional position of Northern Ireland and of course the economic integrity of the single market of the UK as well.
"In that context we made the point that we felt that the current draft EU legal text was not a faithful or fair translation of the joint report from December," said Mrs Foster.
She added: "I also said to him I felt we had made significant progress in December and there was a recognition that we needed to have a frictionless border on the island of Ireland. But there was also a recognition that we needed to protect that market which is so critical for the NI economy, and is so key for us, the UK market.
"We feel that the current draft legal text has omissions in it. It also overreaches in other areas."
DUP deputy leader Nigel Dodds said it was "somewhat ironic to talk about wanting to remove any checks between the border between Northern Ireland and the Irish Republic, and then for the EU to suggest setting up checks and a harder border between one part of the United Kingdom and another part of the United Kingdom".
He added: "It is driving a coach and horses through the EU's own principles about no hard borders."
Mrs Foster also accused the EU of "overreach" in relation to a suggestion that the North-South Ministerial Council, set up under the Good Friday Agreement (GFA), could play a role in terms of the single market continuing to apply where north south co-operation was concerned.
"It talks about giving the North-South Ministerial Council powers. Sorry, the European Union does not have the right to go into the Belfast Agreement in that fashion. The Belfast Agreement has very specific areas in relation to co-operation and those need to be respected," said Mrs Foster.
Following the meeting Mr Barnier Tweeted that "The EU is looking for practical solutions to avoiding a hard border, in full respect of the constitutional status of NI, as set out in the GFA".