Fine Gael and Fianna Fáil have concluded their first round of talks aimed at allowing the creation of a minority government.
The meeting was held in the Sycamore Room in government buildings and lasted an hour and a half.
Afterwards, the two parties issued identical statements describing the encounter as "constructive and cordial".
The Fine Gael team was made up of Frances Fitzgerald, Leo Varadkar, Pascal Donohoe and Simon Coveney. Fianna Fáil was represented by Michael Mcgrath, Charlie Mconologue Barry Cowen and Jim O 'Callaghan.
Both parties agreed to meet again ӻtomorrow.
The Dáil will vote again on Thursday for a new Taoiseach.
It remains to be seen whether that will give the parties enough time to agree a deal that would see Enda Kenny become the first Fine Gael leader to be re-elected as Taoiseach.