Fianna Fáil leader Micheál Martin has said his party will seek to form a government without Sinn Féin.
Both parties have been seeking a path to a viable coalition since the Irish general election earlier in February.
Fianna Fáil's parliamentary party met last Thursday and decided forming a coalition with Sinn Féin "would not be the right thing to do".
On Wednesday, Mr Martin said a steering group would be set up to formally engage with other parties.
He said the group, made up of members of the Fianna Fáil front bench, would begin formal engagements with other parties and co-ordinate the input of their front bench and parliamentary party.
Our party met last Thursday and had a full discussion about what should happen next. We agreed that for many reasons, coalition with Sinn Féin would not be the right thing to do. I have since written to the SF Leader, Deputy Mary Lou McDonald to explain that decision… 2— Micheál Martin (@MichealMartinTD) February 19, 2020
He added that his party - which is the largest in the Dáil (Irish parliament) - had held informal discussions with members of the Green Party, the Social Democrats and various independent TDs (members of the Dáil).
In the election Sinn Féin won the most first preference votes but has 37 seats compared to the 38 held by Fianna Fáil.
No single party has enough seats to govern, with 80 seats required for a majority.
Both Fianna Fáil and Fine Gael - which is led by Leo Varadkar and has been in power since 2011 - have consistently ruled out governing with Sinn Féin, citing its historic links to the IRA as a deterrent.
Mr Martin said he had written to Sinn Féin leader Mary Lou McDonald to explain the decision of his parliamentary party not to negotiate with her party.
She has previously called Fianna Fáil and Fine Gael's decision not to hold talks with Sinn Féin as "quite disgraceful".
Ms McDonald said on Monday her party would intensify conversations with other parties and independents, as it tried to work out if there was a left-wing block and whether it could rule from a minority position.
On Monday, Fine Gael announced its intention to go into opposition following a six hour meeting of its parliamentary party.
Mr Varadkar said if Sinn Féin fails to form a government, then the onus passes to Fianna Fáil.