DUP leader Arlene Foster has rejected Mary Lou McDonald's push for a border poll in the wake of Sinn Féin's election victory.
Sinn Fein won 37 seats in the 160-seat Dail, becoming the second largest party and looking poised to enter into government.
The party also won the highest number of first preference votes with suggestions had the party ran more candidates it could have secured another 11 seats making it the biggest party in the Irish parliament.
Party leader Mary Lou McDonald has now warned that the UK must start preparing for a united Ireland, while also stating the next Taoiseach must push for a border poll.
Irrespective of the view in Dublin or Brussels, a border poll can only be called by SoS if it appears likely to secure a majority in Northern Ireland.— Arlene Foster (@DUPleader) February 11, 2020
No such circumstances exist in Northern Ireland.
2001 GE 42% for United Ireland
2019 GE 38% for United Ireland
She also called for the EU to support Irish unification.
DUP leader Arlene Foster, however, rejected her calls for a border poll indicating support for a united Ireland had declined in the past two decades.
She pointed out that the combined vote for Sinn Fein and the SDLP fell from 42pc in the 2001 General Election to 38pc in the 2019 General Election.
"Irrespective of the view in Dublin or Brussels, a border poll can only be called by SoS [Secretary of State] if it appears likely to secure a majority in Northern Ireland," she tweeted.
"No such circumstances exist in Northern Ireland."
In an interview with BBC Newsnight on Monday, Mary Lou McDonald said Britain and "London in particular" need to start preparing for a united Ireland, because "constitutional change is coming".
"The point has been conceded in the Good Friday Agreement by the British state - the presence here is solely on the basis of consent," she added.
"That consent can only be tested in a unity referendum and we are going to have a unity referendum, and I want us to do it in an orderly, thoughtful, democratic and absolutely peaceful manner.
"Whoever is Taoiseach when all of this plays out needs to make that case very plainly and very clearly to Boris Johnson."
Ms McDonald called on the EU to play its part, stating the bloc "needs to take a stand in respect of Ireland in the same way that it supported the reunification of Germany".
In the context of Brexit, EU leaders have previously said Northern Ireland would have automatic EU membership upon reunification.
Earlier this week, DUP Brexit spokesperson Sammy Wilson argued demands for a border poll would fall on deaf ears.
"They are a foreign country, whatever they say about a UK referendum is immaterial. Any demand from the Republic would be seen as an unacceptable intervention," he said.
"No amount of shouting can change the fact that there is no appetite for it.
"Boris Johnson has been very clear that he won't be giving Scotland a referendum so why would he give Northern Ireland one when that would just invite pressure from the Scottish?"
There has never been a female Taoiseach - in a century, not a whisper of it. Just let that settle for a moment. We've had a number of women as tánaiste, but male leadership of the Irish State has appeared to be a permanent arrangement.