Sinn Féin has tabled a motion seeking to extend presidential voting rights to Irish citizens in Northern Ireland and overseas.
Currently, the Constitution only allows citizens residing in the State the right to vote in presidential elections.
In 2019, the government of the time set a referendum on extending voting rights to Irish citizens living abroad and in the north. However, it was later delayed.
Last May, in the Northern Assembly, a Sinn Féin motion which called for Irish citizens in Northern Ireland the right to vote in presidential elections in the Republic was carried with a majority of 46 to 25.
Speaking in the Dáil tonight, Sinn Féin leader Mary Lou McDonald said it was a "matter of some injustice" and a "violation of democracy" that Irish citizens in the north and living abroad cannot vote in a presidential election.
She told the Dáil: "The president of Ireland is the president for all of the people of Ireland.
"The office of Uachtaráin na hÉireann embodies the shared values and hopes of our citizens, not just here in this State but in the north and indeed across the world.
"It's a matter of some injustice, a violation of democracy that Irish citizens in the six counties and those living abroad are denied the right to vote for their Uachtaráin.
"Citizens from all corners of Ireland who emigrated, many from generations who left due to economic turmoil in search of work, young people today forced out because of the housing crisis, they love their country.
"They have a stake in its future, but they too are denied their vote for president."
Ms McDonald added that November’s election must be the last presidential election that excludes citizens from the north and abroad.
Minister of State with Responsibility for Diaspora Neale Richmond said that the Government would not be opposing the motion.
He said it was not down to simply naming a date for when the referendum could be held, but that a "clear campaign" would be needed.
He told the Dáil: "We all share a long-standing desire to deepen the connections between Ireland and the global Irish, but particularly on this island.
"I want to win this debate because it's the right thing to do."
"This is how we can work together to get this delivered," he added.
Meanwhile, Aontú leader Peadar Tóibín has called for the referendum to be held on the same date as the presidential election later this year.
He said: "It's quite incredible that people (from Northern Ireland) can stand for election, can campaign, and they can even win the presidential election if they are an Irish citizen in Northern Ireland - but they can’t vote in that election.
"We believe all Irish citizens in Ireland, north and south, should be treated equally.
"It would be a sunny day for Ireland and for Northern nationalists if for the first time since 1918 that they get to participate in an all-Ireland democratic process."
Mr Tóibín said that it is unlikely a referendum would be passed before the next presidential election, which must be held on or before 11 November, however, he said the presidential election could double up to include this referendum.
"This would be grasped with both hands by Irish citizens in the north of Ireland. It is not a zero-sum opportunity as well, it doesn't take any rights from unionists, brothers and sisters.
"And also, the power doesn't exist in Westminster or Stormont, the power exists in this building here (Leinster House) to start the process and that's quite significant," he added.
However, Mr Tóibín said that while he was in favour of also extending the vote to Irish people living abroad, this was a separate question that could be looked at down the line.
He said: "I think the very first step we should make sure is that all our citizens living in Ireland, north and south, a person living in Fermanagh shouldn't be treated any differently.
"In relation to the Irish diaspora, that is a bigger decision, and it's a more complex decision in relation to this."
