Fianna Fail and Fine Gael said they have “agreed the need to form a strong, stable government” that will help Ireland recover post-Covid 19.
The statement came after a two-hour meeting between the parties on Wednesday.
The Irish general election earlier this year resulted almost in a tie, with Sinn Fein, Fianna Fail and Fine Gael dominating.
None won enough seats to form a government by themselves, and numerous rounds of talks have so far failed to reach an agreement on a coalition.
Fianna Fail and Fine Gael will meet again in the next week.
In a matching statement, the parties said: “Both Fianna Fail and Fine Gael met this afternoon and had a productive meeting.
“They both agree the need to form a strong, stable government that will help Ireland recover post Covid 19.
“They are working to develop a programme for government that provides stability and majority support in the Dail.
“They will meet again over the coming days and will both continue to reach out and engage with other parties.”
It comes after concerns were raised that further emergency legislation to tackle the spread of Covid-19 cannot be passed without the formation of a government.
Ceann Comhairle Sean O Fearghail has said that without a fully formed Seanad, the Oireachtas cannot pass new laws.
The election of the Seanad will take place next week, however it cannot be fully formed as 11 of the senators are nominated by a taoiseach.
If a taoiseach is not elected by the new 33rd Dail, the Seanad is short of its required 60 members.
It could cause major problems with passing further emergency legislation to deal with the coronavirus outbreak.
Fine Gael leader Leo Varadkar said it is possible to form a government “in the next couple of weeks”.
“We’re not there yet, but we continue to negotiate with Fianna Fail,” he said.
Speaking at Government Buildings before the discussions concluded, Mr Varadkar said: “I think we are going to need a government that’s going to last until 2024 or 2025.
We are working together as a political entity in Dail Eireann to try and help to deal with this unprecedented crisisFianna Fail leader Micheal Martin
“It’s going to need a working majority and that means it’s going to require more than Fianna Fail and Fine Gael.
“Between the two parties, we only have 72 seats. I think for a stable working majority, you’re going to need between 82 to 85.
“So that means having at least 10 more TDs who are willing to come on board, take the whips, stay the course and be willing to make the tough decisions as well as the popular ones for the next four years.
“We’re not there yet, but we continue to negotiate with Fianna Fail, there are discussions happening today and we hope to get to the point where we can then approach other parties to see if they’re willing to form part of that government.”
On Tuesday, Fianna Fail leader Micheal Martin said: “The focus has been on Covid-19 and the crisis that represents to us from a health perspective.
“That is right and proper and my view, as a party leader, has been to support the national effort and not to play politics with this and not play any politics around this virus.
“We are working together as a political entity in Dail Eireann to try and help to deal with this unprecedented crisis.
“That’s how this has to be and talks will continue in terms of the formation of a government.”