Green Party leader Eamon Ryan has said his party will try to get negotiations on a programme for government concluded before the end of the month.
He said the document would then be put to a vote of party members using a postal ballot.
Mr Ryan was speaking after his party agreed to begin formal talks on government formation on Thursday.
A meeting this morning between Leo Varadkar, Micheál Martin and Eamon Ryan began just after 11am and lasted for more than an hour-and-a-half.
The Green Party also published correspondence it received from Fianna Fáil and Fine Gael over the course of the weekend.
It shows those parties pledging that a new government would commit to developing measures to achieve an average 7% reduction in annual greenhouse gas emissions for the next decade.
Meanwhile, the Sinn Féin Leader Mary Lou McDonald has said negotiations which exclude her party cannot lead to a "government of change".
She told a meeting of her parliamentary party that any government led by either Micheál Martin or Leo Varadkar will be about maintaining power and will not deliver the change people voted for.
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Fine Gael leader Leo Varadkar has told party colleagues that he is confident a government can be formed by next month.
Leo Varadkar tells his party colleagues tonight that he is confident a government can be formed by next month. Several TDs and Senators had sought reassurances that FG's core values would be reflected in any programme for government. @rtenews— Mícheál Lehane (@MichealLehane) May 5, 2020
Earlier, Mr Ryan said the talks would take weeks but a government would need to be in place before mid-June.
Today's discussions set out the structure which will underpin those negotiations.
The Green Party will also have to appoint a negotiating team and a reference group.
The talks process will be largely defined by the Covid-19 crisis and the economic recovery plan the virus has precipitated.
Before the meeting, Mr Ryan said he was happy that Fianna Fáil and Fine Gael were committed to meeting more ambitious climate change targets in any future government coalition.
Mr Ryan said this "has to be part of the recovery that we make".
Speaking on RTÉ's Morning Ireland, he said he hopes that any government talks can map the recovery "out of this crisis", learn from it and show solidarity politically and as a people "to map our way out of the bigger crisis of biodiversity loss and climate change".
He said to do this will require "energising local communities and businesses and society" and said that "the other parties recognise and realise that now" and their job is to ensure they get the map right.
Mr Ryan said today's meeting would set a path that sees the economy recovering even as we manage the health crisis into next year and "that will take some time", suggesting a few weeks.
He said any disagreement in his party about entering talks with Fianna Fáil and Fine Gael is "perfectly normal and appropriate politics".
Mr Ryan said while it has been very frustrating for the public to wait for a new government to be formed, over the last three months the Dáil has pulled together behind managing the public health crisis.
The programme for government will also seek to build more social and affordable homes, and hasten the move towards universal healthcare while not increasing income tax.
As these talks progress there will be ongoing communication with several Independent TDs.
Their addition to the three parties is viewed as desirable by some in order to make any new government more durable.
While negotiating the programme for government is likely to prove arduous, gaining its acceptance by the membership of the Greens and Fianna Fáil could be even more challenging.
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Also speaking on RTÉ's Morning Ireland, Fianna Fáil finance spokesperson Michael McGrath said that Fianna Fáil "will leave no stone unturned" and wants to see a durable government formed as quickly as possible.
He said Fianna Fáil would continue to consult with the Labour Party, the Social Democrats and Independents.
Mr McGrath said there was some urgency to get this process under way as a government was needed to agree legislation to put in place emergency schemes to support businesses.
He said a government was needed to take Ireland through to 2025 and to deal with the enormous challenges involved in rebuilding Ireland socially and economically post Covid-19.
Mr McGrath also said there was "no suggestion or prospect" of holding a general election any time soon in Ireland.
He said people cannot leave their homes and the "notion that we can have an election because those elected only three months ago failed to come together is not tenable".
Meanwhile, Tánaiste and Minister for Foreign Affairs Simon Coveney has said he stands over comments he made about protecting farmers and reiterated that he will not sign up to a programme for government that decimates rural Ireland.
Speaking on RTÉ's Today with Sean O'Rourke, Mr Coveney said we should not be talking about quick fix solutions, such as culling the national herd, adding that this is not the aim of the Green Party either.
He said the challenge for the next government is to be ambitious on climate change while also bringing the public with them.
Mr Coveney pointed out that water charges, which were the right thing to do from an environmental perspective, were strongly resisted and there were riots in France, following attempts to introduce a carbon tax.