The Taoiseach says he hopes a joint document on government formation will be agreed between Fine Gael and Fianna Fáil this week or next.
Leo Varadkar says that will then allow them to talk to the Labour Party, Greens, or Social Democrats about forming a coalition.
It comes as the Fine Gael and Fianna Fáil this afternoon held a "positive meeting and discussion on policy issues".
The parties said they "both agreed to keep the dialogue confidential and will be in contact over the next few days".
Mr Varadkar today said he believes a coalition that will last four or five years is needed to deal with the COVID-19 crisis and the subsequent recovery - and that a stable government is needed now.
He said: "There are discussions underway with Fianna Fáil at the moment.
"We'd hope certainly this week or next week to agree a joint document with them, and that would then allow us to approach third parties, like the Labour Party or the Greens or the Social Democrats, to see if they'd be willing to form a government.
"What's going to be required is a government that's going to last for four to five years, that can deal with this crisis, the recovery, and putting our society and economy back when we've got past this health crisis - and that will require three parties and probably the support of independents as well."
He added that he thinks "we're a few weeks away" from a new government being formed.
