DUP leader Arlene Foster has claimed that the draft EU Brexit text is not "faithful" to the EU-UK deal reached in December.
The former first minister said she told EU chief negotiator Michel Barnier during a "constructive" meeting in Brussels yesterday that the text on post-Brexit customs arrangements 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 the UK severs ties with the EU.
Mrs Foster was speaking following a meeting with Mr Barnier in the European Commission. She was accompanied by party colleagues 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," the DUP leader said afterwards.
"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."
The DUP leader said she had told Mr Barnier that she felt "significant progress" had been since December and that she recognised the need 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," she said.
"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," she said.
"The Belfast Agreement has very specific areas in relation to co-operation and those need to be respected."
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".
Sinn Féin president Mary Lou McDonald said taoiseach Leo Varadkar needed to stress to Theresa May that the British prime minister had a responsibility to ensure there are no barriers to trade between the Northern Ireland and Britain.
"The only group threatening to block trade from the north to Britain is the British government," Mrs McDonald said.
"It is clear that the ball is now in British government’s court."
Ulster Unionist leader Robin Swann said he was disappointed that Mr Barnier had not extended an invitation to his party.
"Sinn Féin and the DUP do not speak for all the people of Northern Ireland – there are other parties with mandates who represent the views of a significant portion of our society," he said.
