Last night, the caretaker Taoiseach once again appealed to Micheál Martin to take part in negotiations to form a partnership government.
Enda Kenny also called for an end to Civil War politics.
On Thursday, the leaders of the two biggest parties held a brief meeting, before the Fianna Fail parliamentary party resolutely rejected Fine Gael's proposition.
Mr Kenny has reiterated his belief that a Partnership Government presents the most stable option.
Meanwhile, the Independent Alliance has extended an invitation to both Fine Gael and Fianna Fail to discuss the reality of a minority government.
The alliance says the Fianna Fail leader Micheál Martin has accepted their invitation.
Independent Alliance TD Sean Canney, says it's essential that Enda Kenny and Mr Martin get in a room together to talk about how a minority government could work.
