Taoiseach Leo Varadkar travelled to Áras an Uachtaráin on Thursday night to resign following an inconclusive series of Dáil votes to select the next taoiseach.
He will however remain on in a caretaker capacity until his successor is chosen.
When votes on the candidates for taoiseach were cast by TDs in Leinster House, Sinn Féin leader Mary Lou McDonald received most votes, 45, of any of the four party leaders after a lengthy debate, but failed to be elected.
Fianna Fáil leader Micheál Martin received the second highest vote of 41, followed by Mr Varadkar on 36 and Green Party leader Eamon Ryan on 12.
The votes took place after a lengthy debate following nominations.
Fine Gael’s longest serving TD, Bernard Durkan of Kildare North, said Mr Varadkar was not afraid to take on challenges, including that of leading a minority government.
Mr Varadkar had also led on the challenge of Brexit and as Taoiseach had discharged the office with “distinction, courage and conviction” for the common good of the State.
Fine Gael’s youngest TD, Emer Higgins of Dublin Mid-West, said Mr Varadkar’s leadership on the economy meant another generation would not be standing in airports waving goodbye to their parents.
She praised his courage in his dealings with British prime minister Boris Johnson to achieve a withdrawal agreement and ensure no hard border in Ireland.
Newly elected Kerry TD Norma Foley opened nominations for the Fianna Fáil leader describing Mr Martin as "determined to lead a government" and someone "who will not just to talk about change but who will action it".
She said that in a lifetime distinguished by public service Mr Martin had been true to himself, to his community and to his working-class roots.
Another newly elected Fianna Fáil TD, James O’Connor, Cork East, said the party’s leader had a record on providing progressive change and was known for his perseverance in delivering that change.
Sinn Féin finance spokesman Pearse Doherty said that, if elected, Ms McDonald would be the first female taoiseach and “that in itself is something that really would deliver change”.
The party’s youngest TD, Claire Kerrane, said Ms McDonald had the necessary leadership and charisma to lead the country and was the only nominee who really understood the aspirations and needs of ordinary people.
Nominating Mr Ryan, the party’s Fingal TD Joe O’Brien said the Greens were not into “personality politics” but that sometimes real leadership emerges “not when there is a big shiny prize to be won but when the going is really tough and when there is no thanks or plaudits to be had”.
Solidarity Cork North-Central TD Mick Barry said Fine Gael and Fianna Fáil had been in government for 101 years and were the opponents of real change.
Labour leader Brendan Howlin said there was an element of “pretend negotiations” in relation to the formation of the next government.
Social Democrats co-leader Róisín Shortall said the party would abstain in the vote because it would be meaningless in the absence of an agreed policy platform to lead to a programme for government.
The Dáil is expected to sit again on Thursday, March 5th.