Senior figures from the Northern Irish unionist party including leader Arlene Foster met with Michel Barnier on Tuesday to raise their concerns about the Brexit process, following his meeting with Sinn Fein on Monday.
Ms Foster described the EU's draft withdrawal agreement published last week was unacceptable.
She told a press conference alongside Mr Barnier: "He has put forward an European Union draft text that not only we find unacceptable, the British government finds unacceptable, the Labour party finds it unacceptable, so there will be a need to negotiate from that. It also overreaches in other areas". "That is his interpretation, we don't think it is a fair interpretation of the joint report from December", she said.
"The joint report in its totality needs to be reflected", she said, insisting that the DUP is "ad idem" with British prime minister Theresa May on the issue.
"We will not countenance any proposal which would create a new border in the Irish Sea between Northern Ireland and Great Britain", said Mrs Foster, the DUP leader.
Inside the EU, both Ireland and Northern Ireland are part of the single market and customs union so share the same regulations and standards, allowing a soft or invisible border between the two. Placing a border down the Irish Sea would not just be politically unacceptable but would be economically catastrophic.
Quick guide Why is the Irish border a stumbling block for Brexit?
"We feel that the current draft legal text has omissions in it".
Mr Varadkar added: "We will of course have negotiations about what could be done to avoid a hard border, but what we won't be getting into is a negotiation with the United Kingdom, or a three-way negotiation".
Speaking to RTE's Morning Ireland programme, he said more detail was now needed from the UK Government. "It talks about giving the north-south ministerial council powers. The Belfast Agreement has very specific areas in relation to co-operation and those need to be respected", said Mrs Foster. The European Union's skewed interpretation of "Option C", paragraph 49 of the phase 1 agreement represented one of the most audacious examples of EU encroachment and interference - the very thing many in the United Kingdom disliked and rejected during the EU referendum.