Northern Ireland's power-sharing leaders are split over a proposed all-island forum to deal with the fall-out from Brexit.
First Minister Arlene Foster dismissed calls for a cross-border forum backed by Taoiseach Enda Kenny over the weekend.
But Deputy First Minister Martin McGuinness has insisted there should be "no veto" on the proposed gathering, which would bring together business groups and other organisations on both sides of the border.
Speaking in Dublin at the North South Ministerial Council - set up during the peace process to cement relations - Ms Foster said there was no need for any formal all-Ireland talks.
"I believe that there are more than enough mechanisms by which we can discuss these issues on a north south basis," she said.
"Frankly I don't believe there are any mechanisms needed because we can lift the phone to each other on a daily basis if that were so needed."
Ms Foster, whose Democratic Unionist Party campaigned for a Leave vote, said it was time to "move on" with the UK negotiating in Europe on behalf of Northern Ireland.
But standing next to her at Dublin Castle, Northern Ireland Deputy First Minister Martin McGuinness said all stakeholders, including businesses, should have a forum to put across their views on post-Brexit arrangements.
"I still think the forum suggestion is a good suggestion - I don't believe there should be a veto," he said.
Mr McGuinness said such a body would not undermine any party who did not want to take part.
The Sinn Fein chief, whose party campaigned for a Remain vote, warned Northern Ireland could be "plunged back into the type of situation we were in prior to the Fresh Start Agreement last year" unless there is "collective agreement" on the way forward.
A majority vote in Northern Ireland to remain within the EU "cannot be lightly dismissed" by either the British of Irish governments, he added.
Some 56% of voters in Northern Ireland backed remaining within the EU.
Mr McGuinness also launched an attack on David Cameron.
"London is in chaos, the ruling Conservative Party are in chaos, and isn't it incredible that a British prime minister has resigned against the backdrop of calling a referendum that was driven by Ukip fascists and by the loony right of the Conservative Party?" he said.
Taoiseach Mr Kenny denied he had jumped the gun by suggesting an all-island forum before consulting with Ms Foster, saying he believed there is an opportunity for an "island conversation".
The premier said the body would not be a statutory assembly.
"That invitation is open to everybody but obviously it couldn't function effectively unless you have a buy in from everybody," he added.
Mr Kenny said very serious challenges lay ahead for both sides of the Irish border.
"We are heading into unknown territory," he added.