Fianna Fail will seek to form a government that does not include Sinn Fein, a senior member of the party said today following a meeting of the party's lawmakers.
"We gave the party leader (Micheal Martin) license to speak to whoever he needs to speak to, with the exception of a Sinn Fein," TD Niall Collins told the Reuters news agency.
The party is fully behind the position, he added.
Asked what the likeliest government was now, Collins said "who knows, it may not be possible" to form a government.
Asked if Fianna Fail would talk to Fine Gael about the formation of a government, Collins said, "That wasn't really discussed."
Two of the three largest parties will need to cooperate to form a government, with Fianna Fail on 38 seats, Sinn Fein on 37 and Fine Gael on 35 in the 160-seat Dail, while Fine Gael has already ruled out a deal with Sinn Fein.
The move today raises the chances of Ireland being forced to go to the polls again in the coming months, a development analysts have said could further boost Sinn Fein, whose support surged 50% in last weekend's election in part due to anger at a housing crisis.
Fine Gael and Fianna Fail have long shunned Sinn Fein, citing policy differences and the party's historic links to the IRA, which fought British rule in Northern Ireland for decades in a conflict in which some 3,600 people were killed before a 1998 peace deal.
Both parties are also opposed to Sinn Fein's high-spending promises, its pledge to scrap property tax and plans to hike income taxes on high earners they say would discourage foreign multinationals that employ one-in-10 Irish workers.
Surveys showed that voters rejected the traditional parties over the campaign issues of healthcare and the high cost and low availability of housing, won over by Sinn Fein's high-spending promises and a pledge to freeze residential rents.
Sinn Fein on Thursday effectively admitted it could not enter power without one of the two large parties, with leader Mary Lou McDonald telling reporters it would be "very, very tricky to construct such a government".
Some Fianna Fail lawmakers suggested the party could lead a minority government similar to the previous administration that Fine Gael's Leo Varadkar led via a confidence and supply deal with Fianna Fail.
But Tanaiste Simon Coveney of Fine Gael repeated his personal view that another minority government was not a good idea after both parties suffered in the election.
Another such arrangement between Fine Gael and Fianna Fail would allow Sinn Fein to continue to build in opposition, Coveney told RTE.