Fianna Fáil leader Micheál Martin and Fine Gael leader Simon Harris will hold talks later on the formation of the next government.
The two leaders will also hold talks in the coming days with Labour, the Social Democrats and Independent TDs.
Both Fianna Fáil and Fine Gael have selected their negotiating teams for talks on forming a coalition.
Meanwhile, Sinn Féin leader Mary Lou McDonald has renewed her call for a meeting with the Fianna Fáil leader.
Speaking on RTÉ’s This Week, Ms McDonald said while she had campaigned for a government without either Fianna Fáil or Fine Gael, the worst possible outcome would be a government with both.
She accused Mr Martin of “looking down his nose” at the people who voted for Sinn Féin, saying Fianna Fáil has a decision to make as to whether it wants to put Fine Gael back into government.
“They’re [Fianna Fáil] talking to Independents, they’ve talked to others. Interestingly, the only group that they’ve steadfastly refused to speak to is the second largest party in the Dáil, and I really think for Micheál Martin to look down his nose at over 400,000 people who voted for Sinn Féin and to disregard those votes en masse is really a bad look.”
Mr Martin has previously ruled out going into Coalition with Sinn Féin citing substantial policy differences.
Labour and the Social Democrats held talks about the post-election landscape at Leinster House on Friday.
The Labour Party had called for a centre-left platform to engage with the larger parties as part of talks to form a government.
However, Social Democrats deputy leader Cian O’Callaghan said they would be going it alone and plan to meet with Fianna Fáil and Fine Gael next week.
The Dáil is set to meet on 18 December however it is unclear if political talks will have lead to a new coalition government by then.
