"Exploratory talks" between Fine Gael and Fianna Fáil are to begin next week, it has emerged.
Acting Taoiseach Leo Varadkar and Fianna Fáil leader Micheál Martin spoke by phone late on Thursday evening
They agreed to meet in person early next week for exploratory talks.
Fine Gael has also accepted the offer from the Greens for exploratory talks next week.
A senior Fine Gael source stressed that the mandate from the Fine Gael Parliamentary Party is only for exploratory and consultative talks, not for a programme for government.
The developments come after the Dáil failed to nominate a Taoiseach on the first day of the 33rd Dáil.
Mr Varadkar conveyed to the President his resignation from office.
@LeoVaradkar has formally resigned as Taoiseach. He and his ministers will continue in office as Acting Taoiseach and Acting ninisters until new government is formed #iestaff pic.twitter.com/VsLMrFJ7Ze
— Daniel McConnell (@McConnellDaniel) February 20, 2020
"In accordance with the Constitution, the Taoiseach and the Government will continue to carry on their duties until successors have been appointed," a statement said.