Sinn Fein leader Mary-Lou McDonald has accused the DUP of betraying the public by "pursuing a Tory-led Brexit at any cost".
Speaking at Stormont yesterday, she criticised the "playground rhetoric" of the DUP after Sammy Wilson MP accused Tanaiste Simon Coveney of "belligerent Brit bashing" for advocating an EU/UK customs partnership after Brexit.
Mrs McDonald said the DUP had been "playing games" and stalling for time and insisted a firm resolution to the border problem had to be struck ahead of June's European Council summit.
"The DUP are on the wrong side of the Brexit argument and every time they argue for it, they actually betray the best interests of everybody who lives in the north of Ireland, whether nationalist or unionist," she said.
"They have been found out and are now hiding behind that type of bluster. The more serious issue is the fact that almost two years on from the EU referendum, we still await any sense of a plan or an answer from the British Government in respect of the Irish question."
DUP MEP Diane Dodds said her party would not be taking direction from Sinn Fein.
She added: "It is clear that the Irish government and nationalist politicians in our province wish to use a lack of progress on border solutions to press for the whole of the United Kingdom to remain in the Single Market and the Customs Union.
"Just as Michel Barnier's proposal to annex Northern Ireland in customs terms was roundly rejected, these efforts will fail."
The EU is pressing for "substantive progress" from Britain on the future of the Irish border in time for the crunch summit just six weeks away.
Chief negotiator Mr Barnier told ministers from the remaining 27 member states that "little progress" had been made on the issues of Ireland and governance since the Council last met in March.
His comments came amid continuing uncertainty over the government's preferred option for customs arrangements on the Irish border after Brexit, with a meeting of Theresa May's "war cabinet" thought unlikely to unite behind a solution when they meet today.
Asked about the progress that had been made, Mr Barnier said: "I would say little, not very little."
There were two rounds of negotiations before the "key rendezvous" of the June European Council summit, he said.
Mr Barnier added: "The clock is ticking and we have to conclude and to finalise this agreement ... before October or November, because we have to keep the time for the ratification by the European Parliament, the European Council and the British side."
After talks with Mr Barnier, Mr Coveney again stressed the need for the backstop to be resolved ahead of June's summit.
"Michel Barnier has made it very clear, and I agree with him, that there will be no withdrawal treaty if there isn't a backstop dealing with the Irish border in that treaty," he said.
He added: "Nobody is saying everything has to be resolved by the end of June but we certainly need to see a solution on the Irish border backstop issue taking shape by the end of June.
"There is no flexibility on two things - one, there has to be a backstop in the withdrawal agreement. If there isn't a backstop there won't be a withdrawal agreement.
"And, secondly, that backstop has to deal comprehensively with the border issue. In other words, it has to follow through on the commitment that has been made (in December's joint text) on there being no infrastructure or no related checks or controls on the island of Ireland."