The British and Irish governments have rejected Sinn Féin's call for a border poll in the aftermath of Britain's vote for EU withdrawal.
The Leave campaign emerged as the surprise victor in Thursday's referendum, securing a majority 1.26m voters over Remain.
The vote signals the UK's withdrawal from the EU more than 40 years after joining.
However, while both England and Wales secured majority support for severing ties with Brussels, the electorate in Northern Ireland and Scotland voted to remain.
Scotland voted in favour of the UK staying in the EU by 62 per cent to 38 per cent, while in the north 55.8 per cent supported Remain compared to 44.2 per cent advocating Leave.
The disparity prompted Sinn Féin to call for a vote on a united Ireland – a decision that lies with Secretary of State Theresa Villiers. It came ahead of Scottish First Minister Nicola Sturgeon saying a second independence referendum was "highly likely". The Scottish electorate rejected independence in 2014 by 55 per cent to 45 per cent.
Speaking yesterday, Stormont Deputy First Minister Martin McGuinness said the people of Northern Ireland needed to have a say on their own future.
He said the region was entering "unchartered waters" and he would seek "urgent" talks with the Irish and Scottish governments and EU institutions on "how we move forward in the best interests of all of our people".
"This decision to drag us out of the European Union against our democratically expressed wishes has nothing to do with issues around the European institutions and everything to do with the civil war within the British Tory party," he said.
"The people of the north of Ireland - nationalists, republicans, unionists and others - have made it clear at the polls that they wish to remain in the EU."
He said the referendum result was "to the detriment of all our citizens" and would have an adverse effect on "business, trade, investment and wider society".
But Secretary of State Theresa Villiers said she did not believe the criteria for triggering a border poll had been met.
"The Good Friday Agreement is very clear that the circumstances where the secretary of state is required to have a border poll is where there is reason to believe there would be a majority support for a united Ireland," she said.
"There is nothing to indicate that in any of the opinion surveys that have taken place."
First Minister Arlene Foster cited Ms Villiers as she too rejected the Sinn Féin demand.
"The call for a border poll was as predictable as the flowers in May," the DUP leader said.
"We knew it would come but the test has not been met so therefore I don't believe it will happen."
Ms Foster said the referendum result meant the union was stronger and that she was "absolutely certain" the the region's constitutional status was secure.
Taoiseach Enda Kenny said there was no evidence of a shift in the Northern Ireland electorate that would prompt a border poll.
"There is no such evidence," Mr Kenny said.
"There are much more serious issues to deal with in the immediate terms and that is where our focus is."
The taoiseach said he respected the decision of the British people.
"I want to assure the Irish public that we have prepared to the greatest extent possible for this eventuality," he said.
"There will be no immediate change to the free flow of people, goods and services between our islands."
The Dail has been recalled for Monday to discuss the effects of the Brexit vote on Ireland.
SDLP leader Colum Eastwood called on the Irish government to support Northern Ireland interests in its negotiations with the EU over the UK's exit.
"This will be a devastating blow potentially to our economy and to our society that’s why people in Northern Ireland voted to stay in, that’s why people in Scotland voted to stay in and that’s why young people voted to stay in," he said.
"We’re saying very, very clearly that there should not be any physical or metaphorical border put up across this island we have to make sure that we still allow the freedom of movement people and goods and business right across this island."
