Minister for Foreign Affairs Charlie Flanagan has said that it would be "divisive" and "unhelpful" to hold a border poll on reunification at this time.
Mr Flanagan was speaking at Fordham University in New York, where he delivered a keynote address on Ireland and Europe post-Brexit.
He said that in the context of Brexit it was "important" to keep the issue and reunification "distinct and separate".
He said he stood by the Good Friday Agreement that stated the future of Northern Ireland would be decided only by the people of Northern Ireland.
However, Mr Flanagan said he felt it was "essential" that the unique circumstances on the island of Ireland were factored into a final decision in the Brexit negotiations, saying he did not believe a hard border, or a heavily fortified border, was in the best interests of anyone on the island.
Taoiseach Enda Kenny recently said the prospect of a united Ireland must remain an option in the wake of Brexit.
In an address to the British Irish Association in Oxford University, Mr Kenny said there was no evidence to suggest a border poll would bring about a 32-county republic if held now, but that Ireland should be treated the same as Germany after the fall of the Berlin Wall if people vote for reunification.
He said: "The possibility of unity by consent must be maintained as a valid democratic option into the future.
"That means that, if there were democratic consent to Irish unity at some time in the future, there must be a mechanism to ensure that a democratic decision can be implemented within the European Union, as was the case in Germany."
Mr Flanagan said he would like to see the Brexit negotiations - which he described as "challenging to say the least" - to start as soon as possible as "any prolonged period of uncertainty" was "damaging" and that any delay would not be in the best interests of the UK or Ireland.
In a response to a question from the audience, Mr Flanagan said he felt any attempt by British Prime Minister Theresa May to repeal the Human Rights Act would have the potential to cause difficulty or adversely impact the GFA.
Mr Flanagan affirmed that Ireland was still very much "at the heart of the EU"; that the decision did "not affect Ireland's deep commitment to the EU" and that Brexit actually offered huge opportunities to Ireland.
He said that Ireland would "continue to serve as a gateway to the EU for foreign investors", adding that he knew that US companies were "particularly attracted by what Ireland can offer them", although he did not mention specifically the favourable corporate tax rates.
He said the Government had respected the referendum debate but had been clear in setting out its perspective and on the result he said "we didn't agree with it, we didn't support it, but of course we accepted it".
On the issue of granting a vote to Irish citizens living abroad, Mr Flanagan said he hoped to have a report on how best to proceed with that "during the lifetime of this Government", adding that the Government would then "chart a course" on how best to address the issue.
He said he believed it was "important" that the relationship with the Irish diaspora be "intensified and acknowledged", and said there was no greater way of doing that than by offering a role in the affairs of the State.
