Leo Varadkar and Micheál Martin have decided their parties should "commence in depth detailed" government formation talks.
The two leaders held a meeting today, which followed another meeting last night.
A statement revealed that the leaders held "constructive discussions over the last two days about a series of policy issues and the current political situation.
"They have decided that teams from the two parties should now commence in depth detailed talks."
The statement said that both Fianna Fáil and Fine Gael will "also continue discussions with the Green Party" and that the two parties "enter the talks as equal partners determined to develop proposals which will serve the interests of the people of Ireland."
It added that both Mr Varadkar and Mr Martin are "acutely aware of the enormous challenges facing the country particularly with the onset of Covid-19."
