Democratic Unionist leader Arlene Foster has called for closer Anglo-Irish relations.
In a speech on Brexit in Killarney, Mrs Foster said there are more things to unite than divide Britain and Ireland in phase two of discussions on the UK's split from Europe.
And she suggested leaders across the island of Ireland should work together for the benefit of everyone.
The DUP chief said she planned to raise the prospect of enhancing Anglo-Irish relations, under the auspices of the British-Irish Council, when she meets Foreign Affairs Minister Simon Coveney.
"Maintaining Northern Ireland's economic and political status as an integral part of the United Kingdom is absolutely crucial to me and my party," she said.
"To think anything else would be as foolish as believing that the Taoiseach or the Tánaiste desired anything other than Irish unity.
"But while we will always battle for our own national interests, we must also battle for our mutual interests.
"And our mutual interests will not end on the day the UK formally leaves the European Union. The United Kingdom may be leaving the EU but the common interests that we share across the British Isles will remain."
Mrs Foster made the call at the Killarney Economic Conference in Co Kerry where the issues around Brexit were explored in a two-day conference.
Her suggestions about deepening ties and mutual respect mark a significant departure from the fallout which marked relations between the DUP and the Irish Government towards the end of last year amid both the fractious finish to phase one of the Brexit negotiations and the Irish border question and Mr Coveney's aspirations for a united Ireland.
The DUP suggested Anglo-Irish relations could be deepened through the British-Irish Council, which was set up as part the Good Friday Agreement to improve cooperation between the UK and Ireland in areas such as transport, the environment and energy.
"The UK exiting the European Union ought not to become a barrier to continued co-operation on issues of ongoing mutual interest," she said.
"It especially shouldn't become a barrier when the infrastructure - in the guise of the British-Irish Council - already exists that can allow us to continue to work together as closely as ever on issues of shared interest."
Mrs Foster gave the example of the Nordic Council, which includes Denmark, Finland, Iceland, Norway, Sweden, the Faroe Islands, Greenland and Aland as a means for developing Anglo-Irish relations. She noted that some of the Nordic countries are in the European Union and Eurozone, while others are not.
"Change should not be allowed to weaken the relationships so painstakingly put together across these British Isles," the DUP leader said.
"As challenging as finding a suitable solution might seem, there is no good reason why our own issues on this island should present any threat to the progress we've made.
"I value the relationships we have developed too much to do anything that would jeopardise them.
"But, whether we voted to leave or voted to remain, whether we are citizens of the United Kingdom or citizens of Ireland, we must accept the reality of the referendum result, refrain from the continued re-fighting of the referendum, and seek the sensible, mutually beneficial outcomes from the complex negotiation process ahead that will serve us all well."
Fianna Fáil leader Micheál Martin hheld talks with the DUP leader Arlene Foster earlier today.
"The continued absence of an Executive and Assembly is extremely damaging to Northern Ireland in the context of the Brexit negotiations," he said.
Mr Martin agreed with Mrs Foster's criticism of "megaphone diplomacy" in the heat of Brexit negotiations.
"We need far more considered discussions and engagements. One always has to respect the postion of those you are negotiating with," he said.
"Some of what has gone on has been, in my view, damaging enough in terms of articulating positons too freely in public, to be frank, in advance of negotiations being complete. It's not the way to do business."
Mr Martin added: "I detect from Arlene Foster a clear commitment to the restoration of the Assembly and Executive and a belief that it's the right thing for Northern Ireland.
"In terms of Brexit... I think the focus needs to be on very practical and constructive engagement to mitigate the damage that in my opinion Brexit will do to trade and jobs between north and south and east and west."