But he stressed that the Irish government's position had been consistent throughout. "It would be economic and political madness".
Minister Coveney, whose brief includes a responsibility for Brexit for the Irish government, told delegates at the Slieve Russell Hotel that there can be no change to the regulatory or customs rules which would inhibit cross Border trade.
"I welcome the Prime Minister's commitment on this point".
"Let me urge the foreign secretary to announce a fifth red line today by promising unequivocally what he promised previous year - that Irish border arrangements will not change - and to say that if those arrangements do change, he will refuse to stay in the government".
Mr Varadkar's proposal was also "a fundamental breach" of the GFA's three strand approach to Northern Ireland, which requires a Belfast assembly as well as north-south and east west dimensions, he said.
It last met in 2007.
The Prime Minister will meet Ms Foster and her deputy Nigel Dodds today to discuss restoration of power-sharing before holding separate talks with Sinn Fein president Gerry Adams.
She was reacting to increasingly stark warnings from the EU side that a Brexit with Northern Ireland operating outside the rules of the customs union and single market would have dire consequences for the island's economy and the cross-border provisions of the 1998 Good Friday peace agreement.
"That means convening the BIIGC, as if nothing is devolved then everything is devolved to that conference".
Since January 2017, Northern Ireland has been unable to form a new government.
"I think what maybe has changed is that people are beginning to realise that the Irish government, and the indeed the European Union negotiating team, are insisting on credible answers in terms of how we are going to deal with the Irish border issues in the future in the context of Northern Ireland and Britain leaving the European Union", he said.
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".
"Those in Dublin and Brussels, recklessly trying to use Northern Ireland for their own objectives, should cease".
"We certainly are not seeking to exploit anything".
"It's nearly a faux battle because, actually, the detailed issues will come about when we are talking about the trade issues".