The Democratic Unionist Party has told the EU's chief Brexit negotiator that Northern Ireland must leave the EU on the same terms as the rest of the UK.
DUP leader Arlene Foster, her deputy Nigel Dodds, MEP Diane Dodds and East Antrim MP Sammy Wilson met Michel Barnier in Brussels.
The party told him the EU must show greater flexibility in Brexit talks.
Mrs Foster said it was a "constructive meeting" and that Mr Barnier had "listened to our point of view".
The DUP, the UK and Irish governments and the EU have all said they want to avoid a "hard border" with physical checkpoints on the island of Ireland.
The delegation discussed a draft legal text published by the EU last week, which proposed a "common regulatory area" after Brexit on the island of Ireland - in effect keeping Northern Ireland in a customs union - if no other solution is found.
Mrs Foster said the draft legal text went beyond the joint report agreed by the UK and the EU during a breakthrough in the talks in December.
She said the text had omissions in some areas and overreached in others.
Mr Barnier had been "receptive to that tone", said Mrs Foster, and she urged the UK government to come forward with alternative text for the controversial protocol on Ireland.
The DUP leader repeated a comment made by Theresa May last week, saying that "no British Prime Minister could ever accept the draft legal text".
"It is important that the text accurately and fully reflects December's joint report," Mrs Foster said.
"The fundamental problem as it currently stands is that it challenges the economic and constitutional integrity of the United Kingdom."
The DUP leader also warned Mr Barnier that a 'no deal' scenario would be "more damaging for the Republic of Ireland than for any other EU country".
Mr Wilson said the Irish government was playing Russian roulette because of the risk to their economy if a deal was not reached.
However, Mrs Foster said "sensible solutions" to the post-Brexit Irish border were possible and pointed out: "There already is a border with different VAT rates, fuel duties, currencies and animal health policies."
"Solutions for the Irish border can be found. Importantly though, we need to establish the overall relationship between the United Kingdom and the European Union after the UK exits the EU. It is vital the discussions on trade get underway."
"We will work with Her Majesty's government and the EU27 in delivering a sensible Brexit that everyone wants to see. Today's meeting was a useful part of that process."
Their meeting came after Sinn Féin held talks with Mr Barnier on Monday.
Mr Barnier met Sinn Féin president Mary Lou McDonald, vice president Michelle O'Neill and MEPs Martina Anderson and Matt Carthy.
Ms McDonald said the discussions were a "meeting of minds" and the issue of Brexit was now in "Mrs May's court".
She said the British government had to come up with "Plan A and Plan B".
The Sinn Féin leader added that there could be no overall agreement on Brexit unless the issue of the Irish border was solved.
She said her party was "not looking for a border down the Irish Sea".