British Prime Minister Theresa May pledged on a trip to Belfast on Monday to find a "practical solution" to the Irish border once Britain leaves the European Union.
"Nobody wants to return to the borders of the past," May said after meeting with Northern Ireland First Minister Arlene Foster and Deputy First Minister Martin McGuinness.
"What we do want to do is to find a way through this that is going to work and deliver a practical solution for everybody ... and that we come out of this with a deal which is in the best interests of the whole of the United Kingdom," she said.
Northern Ireland is due to leave the EU alongside other British nations - England, Scotland and Wales - while the Republic of Ireland remains in the bloc. Many fear the island's currently invisible border will have to be fortified.
At the weekend May's Irish counterpart, Enda Kenny, said there "will not be a hard border" on the island of Ireland post-Brexit.
Britain and Ireland have had an open borders travel agreement since 1923, shortly after the southern part of the island gained independence from its former colonial power.