The reintroduction of a hard Border on the island of Ireland cannot be ruled out when Britain leaves the EU, Minister for Foreign Affairs Charlie Flanagan warned on Monday.
The Minister said the possible reintroduction of a border between Northern Ireland and the Republic was a "matter of grave concern" to the Irish Government.
His comments come as sterling fell to a fresh three-year low against the euro on Monday following the announcement by British prime minister Theresa May that her government will trigger Article 50 by March 2017.
Article 50 of the Lisbon Treaty sets out how an EU country might voluntarily leave the union.
Ms May has made clear that the UK will insist on controlling immigration from the European Union after Brexit, even if that means leaving the European single market.
This stance raises the question about how the movement of people across the Border between the North and the Republic will be governed.
Mr Flanagan said he had impressed upon his EU colleagues the “unique situation” in Ireland and “the fact that we cannot go back to the old days of a heavily fortified Border”.
However, he said the scenario of a more visible Border by 2019 “cannot be ruled out”.
The Minister also said UK ministers Boris Johnson, David Davis and James Brokenshire had expressed an “understanding” of the Irish Government’s position.
“I’m not discouraged by what I’m hearing. They don’t want a return to the Borders of the past.”
The pound fell by about 1 per cent against the euro to trade at 87 pence, its lowest level in three years.
Northern Ireland deputy first minister, Sinn Féin’s Martin McGuinness said the UK was facing a “head on collision” with the European Union over Brexit.
Speaking on RTÉ's Morning Ireland, Mr McGuinness said he was concerned and disturbed by the British government's plans to take the UK out of the European Union.
“The Irish government has a very important role to play during those negotiation in representing the democratically voiced wishes of the people of Northern Ireland who want to remain in the EU.
"Our position remains the same, we refuse to be dragged from Europe. We are not going to give in on the issue.
“We are part of a class action in courts to try to prevent being taken out of Europe.
“We want to stay in Europe, we are still trying to maintain that position.”
He added that he had recently met with the Danish Ambassador to the UK and found that there was very little sympathy in Europe to the British government’s position.
Ms May told the Conservative party conference in Birmingham she will invoke article 50 of the Lisbon Treaty before the end of next March, triggering the start of up to two years of formal withdrawal negotiations.
Ms May promised to introduce a Great Repeal Bill next year, repealing the 1972 European Communities Act and transposing all EU laws into British law.
Although the Bill will be presented to parliament before next summer, it will not take effect until after the UK has left the EU.
Ms May said the UK would not follow the model of Norway or Switzerland, which have full access to the single market but must pay into the EU budget and offer free movement to all EU citizens.
“We have voted to leave the European Union and become a fully independent, sovereign country. We will do what independent, sovereign countries do. We will decide for ourselves how we control immigration. And we will be free to pass our own laws,” she said.