Leo Varadkar and Micheál Martin are set to meet again on government formation following a preliminary meeting today - but Fine Gael says it is continuing to prepare to enter opposition.
The Fianna Fáil and Fine Gael leaders met for talks this afternoon.
The Taoiseach is said to have encouraged Deputy Martin to continue to talk with other parties "with a view to forming a government".
Speaking after the meeting, the Fianna Fáil leader said Mr Varadkar "reiterated the Fine Gael position that they want to go into opposition and it's somehow up to others to form a government".
Micheál Martin not ruling out confidence and supply but doesn’t see it as the best option pic.twitter.com/xNkccETdss
— Seán Defoe (@SeanDefoe) February 25, 2020
However, he said the Taoiseach 'didn't reject anything'.
He said there was no talk about the idea of a rotating Taoiseach, and that there’s currently no date set for the next meeting with Leo Varadkar.
However, both parties have this afternoon said another meeting between both sides will happen.
Deputy Martin also said there would not be a government formed by the time the Dáil reconvenes next week.
Meanwhile, Fine Gael said in a statement: "[The two party leaders] exchanged views on a number of matters including housing, climate change, health, cost of living, the economy, and taxation.
"Both sides agreed to meet again at a future point."
However, the statement also notes that the party "continues to prepare for Opposition".
Government formation talks
Micheál Martin is also meeting with independent TDs today.
Denis Naughten of the Regional Group - which consists of nine TDs - said they had a "useful exchange of views" with both Fianna Fáil and Fine Gael earlier today.
He said: "While the group operates as a technical group in Dáil Eireann, the members felt it was imperative they express the views of their constituents that there is now an urgent need to form a stable and effective Government to address the issues facing the country."
Michael Healy-Rae, meanwhile, said he and the Rural Independent Group would be meeting with the Fianna Fáil leader this evening.
Elsewhere, Sinn Féin and the Greens are continuing to hold meetings as Mary Lou McDonald continues her efforts to form a left-wing government.
Green Party leader Eamon Ryan said they would spend today discussing policy under a number of strands - including housing, climate change, health and workers' rights.