The drafting of a framework document being worked on by Fianna Fáil and Fine Gael will continue today.
The document, which could provide a pathway to the formation of the next government, is expected to be signed off when the parties meet again in the coming days.
It is expected the Fianna Fáil and Fine Gael leaders will present this agreed text to the leaders of smaller parties and this could possibly happen before the end of the week.
They will hope to entice them to join a government that will have to deal with the fallout from the Covid-19 crisis and plan for the societal and economic recovery afterwards.
It is understood that increased State intervention in health, housing and childcare will form the key part of the effort to persuade other parties to join Fine Gael and Fianna Fáil in forming the next government.
It is unlikely to be laden with figures and exact targets though given the volatility sparked by the coronavirus.
Instead, it will contain principles that can be added to by other parties and Independents who agree to form a coalition.
Fine Gael leader Leo Varadkar said yesterday that small parties would have to have their core agenda included in any programme for government.
Labour leader Alan Kelly has ruled out going into coalition government, saying it is up to the bigger parties to form a stable, majority government.
He said in the current crisis it is appropriate to talk to other parties, adding "we will talk to anyone who wants to talk to us" but the Labour Party is not in a position to go into coalition.
Speaking on RTÉ's Morning Ireland, Mr Kelly said he wants to put forward the Labour Party’s vision for Ireland, which will show it is different to other parties.
He said he aspires to the party being "very relevant" and will not be "swamped" by Sinn Féin.
Mr Kelly said Labour will concentrate on the social contract with people and will look to allay concerns about housing, the pension age, childcare, health, climate and education.
Fine Gael's Simon Coveney said the document from Fine Gael and Fianna Fáil will give reason to the Green Party, the Social Democrats and the Labour Party to "pause for thought" and consider joining a coalition government.
Mr Coveney said it would show that "politics is certainly going to be different and a national public health emergency demands a different type of governance in Ireland".
Speaking on RTE's Today with Sean O'Rourke, he said the crisis has reinforced the need for an increased role for the State in protecting economic interests and healthcare - essentially moving away from a two-tier healthcare system.
He said Slaintecare committed the Government to doing this, but said it remains a question of "how long it will take and how much it costs".
Mr Coveney said that he does not think a government of national unity would work in the long term and in his opinion would lead to another election in the autumn.
He said that "no one should fool themselves that the Covid-19 crisis is going to be easy to come out off" and it required "compatible parties" at the Cabinet table.
He said Fine Gael is conscious as a government it does not have a majority and is working in the aftermath of an election where the people wanted change.
He said he respects Mr Alan Kelly's official position but said "let's wait and see how he responds" to the proposals.
But he said other bigger parties do need to see what constructive role they will play in helping put together a strong and stable government.
Mr Coveney said that his party believed that it could not sustain a government for four or five years "effectively without an opposition" by including Sinn Féin in a coalition with Fianna Fáil.