Fianna Fáil Leader Micheál Martin has said the next two to three weeks will be key in terms of forming a government and people's willingness to engage will become clear.
Speaking on RTÉ's Today with Sean O'Rourke, Mr Martin said a government made up of three parties with Independents was the best approach and the more secure it can be, the better.
He said that the purpose of the framework document was to "get things moving" and he believes it has created a focus and catalyst for engagement.
He said it was about forming a government and not about personalities and would not be drawn on who would become Taoiseach.
Mr Martin said that he and Leo Varadkar had a broad understanding on a whole range of issues and these will be broached at a later stage.
This afternoon, Green Party leader Eamon Ryan said his party wanted Fianna Fáil and Fine Gael to commit to a 7% annual reduction in emissions.
The party said it would now ask those parties for this pledge following a discussion this morning among its TDs, Senators and MEPs.
A failure to get such a commitment would make it very difficult for the Greens to enter Government, Mr Ryan said.
Mr Ryan said that there were different views in his party on the question of entering formal discussions with Fianna Fáil and Fine Gael.
But he said that they all continued to work well together and would hold a further meeting tomorrow.
The Green Party has 12 TDs, two Senators and two MEPs.
Mr Martin said the overwhelming view of the Fianna Fáil parliamentary party yesterday was to support a coalition with Fine Gael.
He said party members were aware of the unprecedented times we live in and the need to work towards forming a strong government to bring the country out the other side of the crisis.
All parties and Independents have an obligation to form a government because that is the point of an election, he added.
Mr Martin said speed and rapidity of State action in terms of health and housing will be the mark of a new government and having the State more involved in, and leading, in those specific sectors.
The Social Democrats have said their parliamentary party probably will not consider the document in detail until Friday, while the Labour Party has not decided on a date just yet.
Once again TDs were not in position to elect a taoiseach almost ten weeks on from the general election.
Last night the TDs, Senators and MEPs in Fianna Fáil and Fine Gael gave their backing to the document the parties hope will entice others to join them in a coalition government.
Some concern was expressed at both party meetings about how the pledges in the document would be funded.
There were also worries around what such a government would mean for the identity of each party in the long term.
This morning, Sinn Féin's finance spokesperson Pearse Doherty said the framework document is basically "a wish list of vague promises" that contains no specifics but plenty of spin.
He said it contains just one specific - how many trees that will be planted over the next 20 years.
Speaking on RTÉ's Morning Ireland, Mr Doherty said the document does not tell us how many hospital beds will be re-opened or how many houses will be built and if Sinn Féin were to produce a document like this, they would be "laughed out of it" by other parties and the media.
He said there was a huge lack of ambition in some areas, such as childcare and affordable housing.
Call to avoid 'failed policies' of Fine Gael and Fianna Fáil
People Before Profit TD Richard Boyd Barrett has said we must get away from the "failed policies" of Fine Gael and Fianna Fáil in areas such as health, housing and other essential services.
Speaking at Leinster House this morning, he said Fine Gael and Fianna Fáil think the current public health emergency gives them a "divine right" to go back into government.
However, he said the parties inflicted severe damage on the public health service after the 2008 crisis by reducing capacity and staffing levels in hospitals and the country does not need those parties returning to power.
Meanwhile, his party colleague Bríd Smith said the current situation in nursing homes is a "national scandal" and she called on the Government to declare it a national emergency.
Ms Smith said elderly people were put into nursing homes at the beginning of the crisis without being tested for Covid-19.
She said she would question Minister for Health Simon Harris on the issue in the Dáil today.
RISE and Solidarity TD Paul Murphy said Covid-19 measures were not being adhered to in some work places that are deemed essential.
He said there are lots of people still going to work and who feel social distancing measures have not been put in place by employers.
Additional reporting Paul Cunningham and Mícheál Lehane