The party is meeting for a second day for talks with 15 independents and the two Green TDs.
But with suggestions from some of the Independents the talks could drag on forever at their current pace, Fine Gael negotiator and Health Minister Leo Varadkar says they want to put a stable coalition together.
While Justice Minister Frances Fitzgerald says they are respecting the vote of the people by engaging in this process and Junior finance minister Simon Harris says it's still way too early in the process for Fine Gael to open discussions with Fianna Fáil.
As they arrived brothers Danny and Michael Healy Rae criticised up to 40 TDs from Sinn Féin, the Anti Austerity Alliance and others for not taking part in talks.
Talks will continue today and throughout the rest of the week ahead of the return of the Dáil in 8 days for the next attempt to form a Government.
