Fianna Fáil and the Green Party have held five hours of negotiations at Government Buildings during the day on the formation of a new government.
The talks are to resume tomorrow.
Both sides said the talks were cordial and constructive, though difficulties remained to be resolved.
On their way in to the talks, both sides had said there were many issues to be resolved.
After two hours of talks at Government Buildings yesterday, the two parties said while some difficulties on policy issues remained, they would try to resolve these over the coming days.
Both parties described the talks as positive and constructive.
Meanwhile, independent TD Michael Lowry has confirmed that he has accepted an invitation from the Taoiseach to negotiate on the terms of his involvement in a cross-party coalition government.