Negotiating teams from Fianna Fáil and Fine Gael will begin talks tomorrow on government formation following a meeting between the party leaders.
Micheál Martin and Simon Harris described their meeting as "positive" and "constructive".
In a joint statement, they said they had agreed on the need for a stable government "underpinned by mutual respect and clear policy direction, for the next five years, so that it can deliver for the Irish people in face of great challenges".
Earlier, the two leaders contacted Labour leader Ivana Bacik as her party considers its next move in the process.
The deputy leaders of Fianna Fáil and Fine Gael, Jack Chambers and Helen McEntee, will meet tomorrow evening to discuss how the programme for government talks will be run.
This will be followed by a meeting of the negotiating teams from both parties.
A Fiannna Fáil spokesperson said they would engage constructively and positively on the challenges and opportunities facing the country.
Labour adopts holding position following meeting
Labour has adopted a holding position on whether it should enter formal talks on government formation.
Its parliamentary party met today in advance of Ms Bacik holding separate face to face meetings with Mr Martin and Mr Harris later in the week.
Ms Bacik also spoke with the leader of Sinn Féin about future engagement.
The Labour parliamentary party will meet again following these meetings.
It also agreed with Ms Bacik's proposal to write to the leaders of the Social Democrats and Green Party to seek further development of a centre-left common platform.
Labour and the Social Democrats held talks about the post-election landscape at Leinster House on Friday.
Labour had called for a centre-left platform to engage with the larger parties as part of talks to form a government.
However, Social Democrats deputy leader Cian O'Callaghan said the party would be going it alone and plans to meet Fianna Fáil and Fine Gael next week.
January before government formed - Chambers
Minister for Finance Jack Chambers has said he is open to working with both Labour and Independents in a new coalition, adding that he believed it would be early January before a new government is formed.
Speaking in Brussels, the Fianna Fáil minister said: "Policy is the key ingredient that will allow a government to sustain and last for five years. We've worked well with Labour in the past, and other governments have worked well with Labour.
"They've been a constructive voice in the last Dáil, for example, and similarly with Independents, who played a constructive role in the last number of years.
"[I'm] very much open minded to both as an option for government formation, but it really is about policy and how we can put a coherent programme for government together that will work and last for five years."
Mr Chambers said it was too early to say if there could be a coalition between Fianna Fáil, Fine Gael, Labour and Independent TDs.
Arriving at a meeting of eurozone finance ministers, he said: "There are a number of interested parties, and unlike maybe the last two general elections there's a clear route to forming a government, to give political stability and over a period of five years, which I think is centrally important for Ireland, as we face international economic headwinds which are well documented."
Burke warns govt formation 'will take time'
Meanwhile, Minister for Enterprise, Trade and Employment Peter Burke said that no one should put a deadline on government formation talks.
Speaking in Tullamore, Co Offaly, Minister Burke said the priority is to form a stable government and the process "will take time".
"A programme for government is the cornerstone for the future five years" he said.
"We need to ensure it's policy driven and that's where Fine Gael is focused," he added.
The Dáil is set to meet on 18 December. However, it is unclear if political talks will have led to a new coalition by then.
Additional reporting Paul Cunningham, Sinéad Hussey
