Taoiseach Enda Kenny is considering the development of an all-island forum to map out a way forward in the wake of Brexit.
While the plans have been welcomed by the SDLP and Sinn Fein, the Democratic Unionists said the Irish Government cannot speak for the region in any forthcoming negotiations.
The contentious EU referendum result is expected to top the agenda at a North South Ministerial Meeting in Dublin on Monday where political leaders will discuss co-operation on a number of common policies.
SDLP Leader Colum Eastwood said the proposed new forum was essential.
He said: "We believe that it is necessary to consider the issues and implications, not least in terms of helping to develop optimum coherence and consensus on how to minimise the adverse economic fallout and ensure growth on the island.
"We must ensure that any border which is erected is only operational around the island of Ireland, not across it.
"This week we have had confirmation that neither the British Government nor the Northern Ireland Executive have put in place contingency plans to deal with the fallout of the referendum result.
"Here on the island of Ireland, we must map the challenges, purposes and priorities that could most affect us, north and south, rather than following the impulses and bad decisions of the British Government."
Sinn Fein president Gerry Adams also welcomed the plan.
"Subject to seeing the details of the Taoiseach's proposals, I welcome the commitment to establish such a forum," he said.
"Any such forum must have island-wide participation and involve the Assembly parties, the Oireachtas, the European Parliament and civic society.
"The vote of the clear majority of citizens in the North who want to remain in the EU must be respected and defended.
"The Remain vote brought together unionists, nationalists, republicans and others in common cause on the same platform.
"Those who campaigned for a Leave vote should also be invited."
Some 56% of voters in Northern Ireland wanted to stay within the EU while 44% opted to leave.
Overall the UK voted to leave the UK by a slim majority of 52% to 48%.
During an appearance the BBC's Sunday Politics programme, the DUP's Sir Jeffrey Donaldson was adamant that the future of the North should be decided by the UK Government and Stormont Executive.
"The Irish government will not be negotiating on behalf of Northern Ireland - it will be the UK government and the Northern Ireland Executive will be part of that," he said.