At Westminster, Boris Johnson said a hard Irish border would be "madness" as Labour urged him to set a red line or prepare to resign over the issue. "I welcome the Prime Minister's commitment on this".
But the head of the DUP, whose votes the government of British Prime Minister Theresa May is dependent on to pass legislation, repeated her rejection of the suggestion on Monday, saying she would not create barriers to business with the rest of the United Kingdom to allow smooth trade with Ireland.
The DUP negotiator warned Leo Varadkar last night that the agreement required Northern Ireland to determine its own future without external interference.
The BIGC consists of ministers from the British and Irish governments.
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Mr Haass tweeted: "Northern Ireland at a crisis point, the result of poor leadership, Brexit, & a failure to deal with the past. agree that the current impasse likely to lead to restructuring of its politics and/or push for Irish unification. hoping it does not lead to any resumption of violence".
The conference brings together the British and Irish governments to promote bilateral co-operation at all levels on all matters of mutual interest.
Northern Ireland has been without a devolved administration since January, when the governing parties - the DUP and Sinn Féin - split in a bitter row over a failed green energy scheme. It last met regularly during the period 2002 - 2007 when the Stormont Executive was suspended.
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Ireland's Prime Minister Leo Varadkar, pictured arriving to attend the European Social Summit in Gothenburg where he warned he would use veto to force United Kingdom to put in writing commitment to not creating a hard border in Northern Ireland.
Mr Johnson did so, declaring: "There can be no hard border; that would be unthinkable".
Asked if she was accusing the Irish government of being reckless, Mrs Foster said: "I am accusing them of being reckless because if you listen to some of the rhetoric - and look, nobody understands negotiations probably better than I - there are people who will come out and say things to try and push agendas forward".
"It's nearly a faux battle because, actually, the detailed issues will come about when we are talking about the trade issues".
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