Fianna Fáil deputy leader Dara Calleary has said confidence in Northern Ireland politics must be built up again before any prospect of a border poll can be tabled.
Speaking on RTÉ's Morning Ireland, Mr Calleary said there are more important things to worry about now, like getting Stormont up and running, as well as other issues such as health and poverty in the North.
He said confidence in politics needed to be built first, rather than setting arbitrary deadlines that provoke fear with no backup to them.
"Laying down strict timetables on that without building confidence, without confidence-building measures, without building politics or showing politics can work, that will not help the passing of a border poll. I'll make it clear I would like to see a united Ireland, but I want to see a united Ireland based on a united people."
He said unifying people was the most important challenge, rather than having an immediate vote on Irish unity.
Mr Calleary said Fianna Fáil was the party of the Good Friday Agreement, and was in Government at the time and created the conditions for it.
Asked about the possibility of a border poll after five years, he insisted talk of a border poll at the moment was diverting attention away from getting Stormont working.
He said he wasn't arguing against ever having a border poll, but said the notion that it could be done within a set timetable was not helpful to those who had concerns.
He said he would like to see a united Ireland, but only based on a united people, and based on a political system that delivers across the island on issues, and that the system in Northern Ireland was at the moment not delivering.
But Sinn Féin MEP Matt Carthy has said it is deeply disappointing and concerning that Fianna Fáil would hold off on holding a referendum on Irish unity.
Speaking on RTÉ's Morning Ireland, he said it was disappointing that the leader of a "so-called republican party" - Micheál Martin - would rule out allowing the people of Ireland to choose their own future.
Mr Carthy said Irish unity was a legitimate and very progressive aspiration, and it was concerning that Fianna Fáil were holding off on a poll.
"If you believe as I do that a united Ireland will be a better country than a divided country, then you have a responsibility to work for it, and the rhetoric from Fianna Fáil to dismiss those of us who are striving to achieve a united Ireland built on the principles of the Good Friday Agreement is deeply concerning."