"None of them related to the Irish land border, which is a crucial issue to 1.8 million of our own citizens and 4.8 million of our friends south of the Border", she said.
But Lagan Valley DUP MP Mr Donaldson hit back: "We have made it clear to the prime minister and secretary of state that this is fundamentally unacceptable".
Asked if she was warning off Mr Varadkar, the DUP leader replied: "I'm saying to him that he should know better than anybody that you don't play around with Northern Ireland to effect change in other places..." "The Prime Minister should warn Brussels that Northern Ireland must not be used as blackmail". Sinn Fein has said that London is no longer a reliable broker of the Good Friday agreement given the government's dependence on the DUP.
The BIGC consists of ministers from the British and Irish governments.
In a strongly-worded statement ahead of talks in London, Ms Foster said it was "downright careless" to suggest leaving the European Union would cause a return to violence not seen since the Troubles.
Mr Varadkar had called for the recall of the bilateral body, a construct of the 1998 GFA, which brings together United Kingdom and Irish ministers to encourage cooperation on matters of mutual interest.
Sinn Fein's Pearse Doherty asked Mr Varadkar about the conference during exchanges in the Dail yesterday.
It comes as Theresa May was due to meet Northern Ireland's leaders at Downing Street over the ongoing power-sharing crisis at Stormont, which has been without a functioning administration since January.
The DUP leader, Arlene Foster, said it was a "talking shop which has not met since 2007".
The former First Minister accused leaders of "recklessly trying to use Northern Ireland for their own objectives" just days after Taoiseach Leo Varadkar said Dublin would try to block European Union trade talks unless it received a guarantee there would be no hard border on the island of Ireland.
He had previously served as special envoy to Northern Ireland under the presidency of George W Bush. "I think that message is understood and I'd anticipate progress in the coming weeks".
She added: "Some people are taking their moment in the sun to try and get the maximum in relation to negotiations".