Both Fine Gael and Fianna Fáil have announced that the parties will meet early next week to discuss how a minority government would work.
The statement came after exploratory talks between the two parties earlier today.
The Taoiseach left Government Buildings at around 6pm. It is understood that he spent the afternoon there as efforts were stepped up to overcome the obstacles to forming a new government.
Both parties released short statements tonight saying that negotiating teams would begin talks early next week.
Significantly, the focus will be on how a viable minority government would work. The Taoiseach's preferred option has been for an equal partnership government.
The shape of the next government may become clearer when the Dáil meets again on Thursday.
Independent TDs were not involved in today's talks and each party will continue separate parallel talks with them.
Independent TD Michael Healy-Rae welcomed the announcement that talks will take place between the two main parties and said anything that steers the country away from another "costly" general election is good.
The Kerry TD said he will continue to talk to both parties ahead of what could be the key vote in the Dáil next Thursday.
Independent TD Shane Ross said a big roadblock to forming the next government has been removed and he said the talks were what the Independent Alliance had called for all along.
He said they would continue talking to both sides and would decide accordingly who to support.