Sinn Féin is calling for a poll on Irish unity.
The call comes following the UK vote to leave the EU, although in Northern Ireland a majority voted in favour of staying.
Sinn Féin says that the decision by the UK to leave the EU will have "massive ramifications on the nature of the British state", given Scotland also voted Remain.
In Northern Ireland 440,707 (56%) people voted to Remain and 349,442 (44%) voted to Leave.
Sinn Féin's national chairman Declan Kearney said the question of Northern Ireland remaining as part of the UK had now been brought into sharp focus.
Of the North's 18 constituencies, 11 voted Remain and seven (all unionist strongholds) voted for Leave
A border poll can only be called by the Northern Secretary in circumstances where there is clear evidence of a public opinion swing towards Irish unity.
Mr. Kearney told the BBC: "We have a situation where the north is going to be dragged out on the tails of a vote in England."
He added: "We now have a situation where Brexit has become a further cost of partition, a further cost of the Union and Sinn Féin will now press our demand, our long standing demand, for a border poll."
Meanwhile, the DUP's Sammy Wilson has welcomed the Leave outcome.
He said: "The future for Northern Ireland will be as bright as the future of the United Kingdom is going to be."
Northern Ireland is now set to become the only part of the UK with a land border between it and an EU member (the Republic of Ireland).
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