Fine Gael and Fianna Fáil say they will meet again in the coming days as efforts continue to form a new government.
It has been revealed no new laws can be passed from next week because approval of both the Dáil and Seanad is needed.
Seanad elections are underway but 11 members must be chosen by the Taoiseach, and that canot happen if the current Taoiseach is outgoing.
Fine Gael and Fianna Fáil say they need to form a stable government to help Ireland recover post-Covid 19.
In a statement, Fianna Fáil said the parties hadh had a “productive” meeting this afternoon, and both agreed the need to form a “strong, stable government”.
The parties “are working to develop a Programme for Government that provides stability and majority support in the Dáil”, the statement says.
They will meet again over the coming days and will both continue to reach out to other parties.
Earlier, Green Party TDs ruled out any government formation talks with Fianna Fáil and Fine Gael as the Covid-19 crisis continues, insisting a unity or national government is required.
The party has come in for criticism for advocating a cross-party government at a time of national crisis, but TDs have argued that rather than cause confusion, such a government would address the pressing issues facing the country.