Brendan Howlin has announced his resignation as Labour leader after the party decided that it will not play any formal role in the next government.
A leadership contest will get under way in the coming weeks.
Speaking after a meeting of the Parliamentary Labour Party (PLP) at Leinster House yesterday, Mr Howlin said the party did not receive a mandate to enter any government in the 33rd Dail.
However, he did not rule out the party supporting certain policies from opposition.
Mr Howlin met Green Party leader Eamon Ryan yesterday to discuss policy co-ordination and has also held talks with the leaders of the Social Democrats and Fianna Fail leader Micheal Martin in recent days.
He declined to be drawn on his discussions with Mr Martin.
Labour's executive board will meet this weekend to approve arrangements for the election of the next leader. Any candidate who wishes to enter the race will need a nomination from another TD or senator.
Among the contenders likely to throw their hat into the ring are former deputy leader Alan Kelly, who was unable to secure a nomination to challenge Mr Howlin for the leadership four years ago.
Mr Kelly is likely to face competition from Aodhan O Riordain and Ged Nash, who both regained Dail seats they lost four years ago in last weekend's General Election.
Mr Nash declined to be drawn on his intentions yesterday.
"It's Brendan's day," he said.
Mr O Riordain and Mr Kelly did not respond to calls. Another potential contender, Cork East TD Sean Sherlock, is understood to be ruling himself out of the contest.
Speaking at a press conference in Dublin yesterday, Mr Howlin said: "It has been an honour to lead the Labour Party but now is the right time to pass on the baton to a new generation.
"It has been undoubtedly a difficult election for us but I believe we have succeeded in sowing the seeds for future growth."
Mr Howlin failed to improve on Labour's worst-ever election result having assumed the leadership from Joan Burton in 2016.
The party returned six TDs in the General Election - one fewer than it had in the last Dail.