Taoiseach Enda Kenny has held a meeting with the Social Democrats as preliminary negotiations on the formation of government continue two days ahead of the first meeting of the 32nd Dáil.
In a statement, the party, which won three seats in the General Election, described the meeting as constructive, with broad agreement on the need for Dáil reform.
"We listened carefully to the Taoiseach's proposals but we also made it clear that while most of the conversations happening are about the make-up of the Dáil, there are significant crises affecting people's lives on a daily basis and they must be addressed urgently," co-leader Stephen Donnelly said.
The group, which includes Shane Ross and Finian McGrath, gave Fine Gael its position paper on supporting any government at a meeting on Friday.
A spokesperson for the Independent Alliance this evening said the group had met with Fine Gael representatives this afternoon.
In the meeting with Mr Kenny, Simon Coveney, Frances Fitzgerald, Simon Harris, Leo Varadkar and Eoghan Murphy, the alliance "went through our Charter for Change in great detail and agreed to exchange documents and engage in further dialogue, at an early date".
At the weekend, Mr Ross described Taoiseach Enda Kenny as a "political corpse" and yesterday stood by those comments.
Mr Kenny has said that the indications were that nobody would be elected Taoiseach on Thursday when the Dáil returns.
Deputy John Halligan, who is part of the Independent Alliance, said that he will not be offering any preference for Taoiseach on Thursday, unless there is a programme for government.
Meanwhile, Minister for Transport, Tourism and Sport Paschal Donohoe has said that, as the largest party in the Dáil, Fine Gael has a responsibility to put together a new government but it cannot be put together at any cost.
Speaking on RTÉ’s Today with Sean O’Rourke, Mr Donohoe said that he would not put a timeframe on any discussions but he thought that there were many weeks of discussions ahead.
He said that Fine Gael did not want to put a government in place that would erode the progress made so far.
Mr Donohoe said it is “very likely” that consideration will have to be given to how Fine Gael engaged with Fianna Fáil, but ongoing discussions with other parties must be considered before that happens.
He said that a government can be put in place without Fianna Fáil.
Fine Gael is also meeting, separately, Independent TDs Maureen O'Sullivan and Katherine Zappone today.