Sinn Féin has said comments made by the Taoiseach on Irish unity are "shortsighted and out of step".
Speaking in a pre-Christmas briefing, Leo Varadkar said that he does not think a border poll is a good idea.
He said parties in Northern Ireland that supported a united Ireland did not have a majority, at around 40%, adding that was why he was opposed to holding a poll on Irish unity now.
The Taoiseach has previously ruled out sponsoring a forum on Irish unity in anticipation of a poll on abolishing the border, arguing that such a move would be divisive and provocative to unionism.
However, Sinn Féin's spokesperson on Justice and Equality, Martin Kenny, said recent polls have shown a majority in Northern Ireland "have indicated that there is now a real demand for a United Ireland."
Mr Kenny said the Government needs to "bring forward a Green Paper on the issues that need to be addressed to tackle the hangovers of partition."
He added that it is "high time" that the Government begin "meaningful engagement" with the British government to arrange a date for a referendum on Irish unity within five years.
"The issue of Irish unity is not going away, no matter how much the Taoiseach may want it to," Mr Kenny said.
"His comments today are utterly shortsighted, are out of step with the electorate, - north and south - and do not reflect the reality of where people are at."
Meanwhile the leader of the Green Party has dismissed calls for a border poll over a united Ireland, which he says risks being divisive and counterproductive.
Eamon Ryan said his party, which has representatives on both sides of the border, does not think it is the right time for a border poll.
"We don't think it is time for a border poll. Why would you repeat the mistakes of Brexit?
"Why force a question through where you haven't even worked out what the possible answers might be, or even what question you ask?"
"That is something that we have learned in the South over the years, that referenda are difficult things and can go wrong. People answer the wrong question or answer different questions than were asked."
"I just don't think, at this present time, that's the number-one priority. I think the number one priority should be getting Stormont back and reforming the way it works, making sure it actually is much more representative."