The Regional Dáil Group has called for a deadline to be set for smaller parties to declare if they intend to enter talks on government formation.
The call was made by two of the group's TDs, Michael Lowry and Denis Naughten, who were part of a delegation that met with Fianna Fáil and Fine Gael this afternoon.
Fianna Fáil and Fine Gael today spoke to 11 Independent TDs as the work of forming a new government intensified.
The Fianna Fáil Deputy Leader Dara Calleary described the meetings as positive.
Independent TDs heard today that Minister for Finance Paschal Donohoe will deliver a warts and all assessment of the economy next Wednesday.
This economic update is likely to provide many answers for those weighing up the decision to join government formation talks.
Today's discussions with groups of Independent TDs were described by Fine Gael and Fianna Fáil as good and further talks are on the cards.
The need for a third political party to join any new government was a point emphasised repeatedly by the Fine Gael side, sources have indicated.
But the regional group, which has eight Independent TDs, stressed that there needs to be more urgency injected into the process.
Its TDs said that ten weeks on from the election people want certainty.
The group's other deputy, Aontú Leader Peadar Toibín will meet Fianna Fáil and Fine Gael later in the week.
Sligo-Leitrim TD Marian Harkin of the Independent Group described today's meeting as a first date and said there would be further ones.
Her group colleague Michael Fitzmaurice said the response to Covid-19 is the key priority, but any programme for government must also place an emphasis on agriculture and regional development.
Clare TD Michael McNamara also attended the meeting.
Meanwhile, Sinn Féin Leader Mary Lou McDonald addressed a meeting of her parliamentary party this evening.
She told them that other scenarios could still unfold despite the Fianna Fáil and Fine Gael policy agreement.
Ms McDonald said that those parties had excluded Sinn Féin but her party has not given up on forming part of the next government.
Fine Gael has said a third party is essential in any government in addition to Independent TDs.
The party also said it is open to Independent TDs being a full part of government as part of a formal agreement.
Fine Gael and Fianna Fáil have 72 seats between them, but a majority of 80 is needed to form a government.
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They are hoping to entice smaller parties, including the Green Party, the Labour Party and the Social Democrats, to increase their Dáil numbers.
The Green Party has 12 seats, Labour has six, the Social Democrats has six and there are 19 Independent TDs.
The Green Party is meeting remotely today to work on a response to the Fianna Fáil/Fine Gael joint policy plan.
The party said it wants more clarity on issues such as carbon emissions and housing.
Fianna Fáil said a letter would be issued to the Social Democrats today in response to its queries about the economic projections in the plan. Fine Gael said it would respond in due course.
The Labour Party said it is up to other parties to form a government, but it said it would continue to review the Fine Gael/Fianna Fáil plan this week.
Additional reporting Aisling Kenny