Fianna Fáil and Fine Gael will begin full negotiation talks for forming the next Government today.
The two parties' deputy leaders, Jack Chambers and Helen McEntee, met last night to discuss the structure for today's negotiation talks.
Both sides said it had been a "positive engagement" and full talks will take place today with discussion turning to Government formation.
Fianna Fáil and Fine Gael will also meet with the Social Democrats - who are down to 10 TDs following the suspension of Eoin Hayes.
The newly elected Dublin Bay South confirmed that he will sit as an independent in the next Dáil, after misleading the media regarding shares he had in a company which has links to the Israeli Defence Forces.
Meanwhile, Ministers in the outgoing Government will meet this morning for the first meeting of the Cabinet since the General Election.
Independents
As Government negotiation talks get underway, it is looking increasingly likely that the next Government will consist of a coalition between Fianna Fáil, Fine Gael and a number of independents.
Fianna Fáil will have the most TDs in the next Dáil after they secured 48 seats in the General Election.
Sinn Féin emerged as the second biggest party with 39, while Fine Gael will have 38 TDs in the next Dáil.
Yesterday, Fine Gael leader Simon Harris met with independent TDs Gillian Toole and Sean Canney.
Fianna Fáil leader Micheál Martin, meanwhile, had a lunchtime meeting with Ivana Bacik.
It is understood that Sinn Féin will meet other parties as the week continues.
Feature image shows Simon Harris and Micheál Martin, photo by Leah Farrell, RollingNews.ie
Additional reporting by Stephanie Rohan.