FINE Gael will "ramp up" efforts to form a government over the coming days as negotiations with the independents bloc are expected to continue.
Tuesday saw Enda Kenny's party take part in a second day of discussions with 15 independents and the two Green Party TDs.
The Dáil will convene again a week on Wednesday - almost seven weeks after southern voters went to the polls.
Mr Kenny, whose party emerged from last month's election significantly short of a majority in the Dáil, is expected to have agreed a minority coalition deal before contacting Fianna Fáil leader Micheàl Martin.
Ahead of yesterday's meeting, acting Minister of State Simon Harris said: "The Taoiseach has made it clear that at some point it will be necessary for whoever proposes to form a government to talk to the people on the opposition.
"It obviously makes sense that you would talk to the people who want to be in that government with you."
But independent TD Micheal Healy-Rae said it was disgraceful that the Dáil's two main parties had not spoken yet.
He said there was concern among the independents that they were being used by Fianna Fáil and Fine Gael.
"We do not like being used as leverage in that way," the Kerry South TD said.
Minister for Health Leo Varadkar said the talks with the independents and Greens were going "reasonably well" but he also suggested it would be difficult to form a stable government without "some sort of arrangement" between his party and Fianna Fáil.
"There’s very good debates happening, very good talking," he said of this week's discussions.
"A lot of common ground, but it’s a very diverse group... involving two parties, Fine Gael and the Greens but also independents of all hues - urban, rural, left, right and centre. So I don't think it's something that can be concluded quickly, but could potentially be concluded by next week."
Mr Varadkar, who is part of the Fine Gael negotiating team, said his party would intensify and "ramp-up" its efforts to form a government this week.
