The Sinn Féin leader Mary Lou McDonald has said the idea of a rotating Taoiseach would have to be a part of any government formation talks.
Ms McDonald said she is beginning the process of trying to form a government without Fine Gael and Fianna Fáil as her Ard Comhairle meets tonight.
It looks as though no party will get more than 40 seats in the next Dáil.
With Fianna Fáil likely to be just a few seats ahead of Sinn Féin, Ms Lou McDonald said the idea of a rotating Taoiseach would have to be considered if they went into coalition.
Speaking this evening she said: "I have been informed by my office in Cabra that I'm now the Taoiseach of Cabra.
"We won the popular vote, we won the election.
"I'm not a bit presumptuous about positions or office or any of that but I certainly don't presume that I will be Taoiseach and I don't think anyone should make that presumption either."
"Obviously, that would have to be part and parcel of a discussion around a discussion that we have around a government formation.
"For what it's worth, I think it would be a mighty thing to have a Sinn Féin Taoiseach, and also a woman in the job, but you might say 'she would say that, wouldn't she'."
She also said she has spoken to Eamon Ryan, Brendan Howlin, the Social Democrats and Solidarity - PBP about forming a government and is keen to speak to a number of Independent TDs.
Mary Lou McDonald says she’s been dubbed “The Taoiseach of Cabra”.
Adds that the idea of a rotating Taoiseach would have to be on the table in any coalition negotiations #GE2020 pic.twitter.com/e6DYOXX7KI— Seán Defoe (@SeanDefoe) February 10, 2020
The Sinn Féin President was joined with David Cullinane, a newly-elected TD in Waterford, in addressing the media.
Mr Cullinane defended comments he made to supporters during a celebration event in the constituency yesterday.
He shouted the words 'Up the Republic, Up the Ra, Tiochfaidh ár Lá' at the end of his victory speech.
Mr Cullinane told Today FM that his comments were in relation to Kevin Lynch, a hunger striker, and refused to make any apologies.
Sinn Féin’s David Cullinane explains his comments at a celebration last night where he said “up the Ra” #GE2020 pic.twitter.com/tpOxf3mQ3o
— Seán Defoe (@SeanDefoe) February 10, 2020
Speaking alongside his party leader tonight he said: "My comments were about the past, they're not about the future."
He said: "The IRA is gone, as everybody knows and I celebrate that the same as anybody else, and we have a very successful peace process.
"I don't feel I have to apologise for reflecting back on that time period, what I'm saying is I'm putting context on the comments that I made.
"I in no way meant that this was about the here or the now or the future.
"I was reflecting back on what was a very emotive time for Republicans and as someone who stood in a constituency where a hunger striker previously stood in, in the context of a long campaign, a long day and a long night I think that's the context in which the comments were made
He added: "I think most people will see that, I certainly don't set out to offend anyone."
