The Labour party is meeting this afternoon for the first time since the general election
The Green Party has walked out of talks on forming a coalition.
Party leader Eamon Ryan says the make-up of the Dáil means Fine Gael and Fianna Fáil should work together - and anything else is a delay.
It comes as both Fianna Fáil and Fine Gael are holding separate meetings with Independent TDs today as efforts to put together a government continue.
Greens and Independents met with Fine Gael yesterday as Enda Kenny's party offered a possible deal on housing - but marathon talks broke up without any progress reported at 9.00pm last night.
Negotiations resumed at around 8.30am this morning.
Fine Gael has said it will not be making contact with Fianna Fáil until it sees what its position is with these groupings.
However, the Green Party has now withdrawn from talks with Fine Gael.
Eamon Ryan says he had hoped other parties would have joined the discussions.
He suggests that while the negotiation process is very useful, "the numbers dictate where the actual possibility of stable government lies... We were very keen to try and get other parties in".
He adds that if there is an intention to put together a rainbow coalition, "it has to be a rainbow".
Speaking to Newstalk Lunchtime, Fianna Fáil's Willie O'Dea said "I think it has been acknowledged by Leo Varadkar that whatever deal is done... they will need some sort of understanding with the other group - the group that doesn't get the majority of independents - to bring some element of stability to the government".
He also explained that "our negotiators will meet with [independents] and we will let them put questions to us with their concerns... I think that's a much more efficient and businesslike way to do things".
The acting Transport Minister Paschal Donohoe earlier suggested that Independents would not be wasting their time with long talks if they did not think a deal could be reached.
Separately, the Labour Party is meeting this afternoon for the first time since the general election, when the party lost 30 TDs.
Joan Burton yesterday said there will be a "very open" discussion about her leadership at the parliamentary party meeting.
The party has already confirmed it will not be part of formation of a new government.
Independent Kerry TD Michael Healy-Rae has suggested that another election could be called as early as May 20th.