The British government is being asked to grant UK passports to people born in the Republic but who have lived in the north for some time.
One of the highest profile cases of a long-term Northern Ireland resident born across the border is assembly speaker William hay.
The DUP MLA was born in Donegal just a year after the south became a republic, which means that unlike those born before 1949 he is not entitled to a British passport.
First Minister Peter Robinson and Deputy First Minister Martin McGuinness have confirmed that they will write to the authorities in Britain and make representations on the issue.
The Stormont leaders' confirmation came in a written answer to a question from DUP MP and MLA Gregory Campbell.
Mr Campbell told The Irish News that while everyone in the north was entitled to apply for an Irish passport there continued to be an "unfair situation" where not everyone in the region is eligible for a British Passport.
"Those people who were born in the Republic of Ireland after 1949 but live in Northern Ireland do not qualify for a British Passport," he said.
"This leads to the situation where thousands of people including the current speaker William hay for example, are all unable to obtain a British passport."
The east Derry MP said the issue had been a long-running concern for him.
"We have raised this issue on many occasions but to date there has been nothing done to accommodate those people born in the Republic of Ireland but who have lived in northern Ireland for decades and may wish to apply for a British passport," he said.
A spokesman for the Department of Foreign Affairs in Dublin said: "eligibility for British citizenship is a matter for the relevant British authorities and questions relating to British citizenship should be addressed to them."
A new Irish passport, which includes verses in Ulster Scots and features a map of the entire island for the first time, was launched on Monday. extracts from the Irish constitution stating the birthright of anyone born north or south of the border to be part of the Irish nation are also prominent throughout the redesigned passport.
Tanaiste eamon Gilmore has played down any significance in the inclusion of a map of the island.
"It's a topographical map... it is not intended to be a map of the administrative or political arrangements," he said.
Dismissing any suggestion of territorial connotations, Mr Gilmore said that the Republic's government did not consult with Northern Ireland Secretary of State Theresa Villiers about any aspect of the revamp.
The first of the new passports will be issued on Thursday.
