The Green Party is to enter formal talks with Fianna Fáil and Fine Gael, with a view to developing a programme for government.
Its Parliamentary Party made the decision after a meeting today.
Both Fine Gael and Fianna Fáil have agreed to enter government together - but need a third party to make up numbers in the Dáil.
During the week the Greens set out its demands - however a key target of reducing carbon emissions by 7% was not agreed in a response.
On Friday, Taoiseach Leo Varadkar said it was something he would like to work towards.
He also said he is hopeful a new government can be in place by June.
In a statement, The Green Party said: "We are conscious of the huge challenges facing any Government in the COVID-19 crisis.
"The party will now work with Fianna Fáil and Fine Gael to develop a deal that respects our mandate with a view to presenting that agreement to Green Party members for approval."
It added: "Green Party approval of any programme for government will require support of 2/3 of the Green Party voting membership.
"Any proposal must be transformative on climate action and commit to strong progress towards a more sustainable and fairer society.
"If this is not the case Green Party representatives will withdraw from negotiations and pursue their mandate in opposition and work to hold the government to account."
Green Party leader Eamon Ryan says he'll will seek a meeting with the Fianna Fáil and Fine Gael to start the process.