The Labour Party will continue talks with Fianna Fáil and Fine Gael, but its leader says it is "unlikely" it will enter government.
The party met on Friday to discuss preliminary government formation talks it had held with Simon Harris and Micheál Martin and said that it will seek "a substantive response" to its priorities for a government.
When pressed on the issue on Friday, party leader Ivana Bacik said that the party may not have the "leverage" to influence real change given that Fianna Fáil and Fine Gael have a total of 86 seats between them, two short of a majority.
Ms Bacik said that it was "unlikely" that Labour would join the two outgoing coalition parties in government but wanted to give each leader the chance to outline their proposals. Ms Bacik denied that her party was worried about being the first to step away from negotiations.
"We're very conscious of the reality of the gulf between our policies and of the very small gap between the two big parties and an overall majority, meaning therefore that we would have very little capacity, influence, or leverage to deliver on the ambitious program for change we want to see.
"We're realistic about the numbers. We're realistic about the lack of leverage that any smaller party going in to a governing coalition with two big parties that has 86 seats between them."
Labour's government priorities include a more active role for the State in issues like housing, a "focus on investing in public services and infrastructure over unsustainable tax cuts that narrow the revenue base" and a "massive street-by-street retrofitting programme for homes".
However, Ms Bacik said that a newspaper report based on notes of a party national executive meeting which said that she was against going into government was not "an accurate reflection" of the meeting.
She said that she had asked the party's secretary general Billie Sparks to establish who had leaked the details of the meeting, saying that whomever leaked it would be expelled from the party.
Meanwhile, with Fine Gael continuing to engage with Fianna Fáil, the Social Democrats and a group of independents on forming a government, Mr Harris said that he believes a government can be formed next month.
During the election campaign both he and Tánaiste Micheál Martin said that they would like to see a government in place by the January 20 inauguration of US President Donald Trump.
With Fianna Fáil and Fine Gael members having to vote to pass a program for government, that window is beginning to close, but Mr Harris said there will be "no dilly dallying" on his party's part.
"I would like to see a government in place in the month of January. I think that is still possible, but it's important that the policy is right, and that's where our focus will be. So we will not be found wanting in terms of putting in the long hours, the hard yards to get this right.
"But I'm long enough at politics now to know that what goes in the program for government matters. It becomes the blueprint for the next five years, the direction of travel for the next five years, not just for politicians and government, but also for official Ireland, for the civil service, for the public service."