Calls have been made to open Irish passport offices in Belfast and Londonderry after the Brexit vote sparked a surge in demand.
SDLP MLA Nichola Mallon said the Stormont Executive should help facilitate the move.
She said: "Given the stated will of the people of Northern Ireland, it's critical that we accelerate the process of north/south integration and co-operation.
"One early way of advancing that project is to establish passport offices in Belfast and Derry to meet the surge in demand for Irish passports as people here seek to protect their European citizenship and entitlements.
"The Executive must provide resources to ensure that happens immediately."
One in four people in Britain has Irish heritage.
Anyone born on the island of Ireland or whose parents are Irish automatically qualifies for citizenship.
In some cases, those who have an Irish grandparent can also apply.
The Republic's Department of Foreign Affairs has issued an appeal for calm after Post Offices ran out of Irish passport applications in the wake of the referendum result.
Foreign Affairs Minister Charlie Flanagan said the spike could have a significant impact on the passport service and could hit those who urgently need one.
In Northern Ireland, 56% of voters supported staying in the EU.
Overall however, the UK decided to give up its EU membership with a slim majority of 52% to 48%.
Meanwhile, Sinn Fein president Gerry Adams said a national forum should be set up to discuss the impact of the Brexit vote.
He said: " This forum should aim to have island-wide participation and involve the Assembly parties, the Oireachtas, 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.
"There is an imperative on all of those who are concerned about the consequences of the Brexit vote to work together in the time ahead."
In a statement, the Irish Department of Foreign Affairs said: " The vast majority of passport applicants on both sides of the border submit their passport applications through the Post Office network on this island.
"This is the most efficient and cost-effective way to apply."