Acting Taoiseach Leo Varadkar has said his party is preparing for opposition ahead of a meeting of TDs later.
He says he will only consider entering government as a last resort.
Fine Gael's Parliamentary Party will meet for the first time since the election on Monday to decide what its next steps should be.
Mr Varadkar has been consulting with all successful and unsuccessful election candidates about what they should do.
This morning he said the party is preparing for opposition - and that it will only enter government as a last resort.
Mr Varadkar says that Sinn Féin should try to put together a left wing government, and that Fianna Fáil should try to form a rainbow coalition with The Greens, Labour, the Social Democrats and Independents.
He added that Fine Gael will only consider entering government as a last resort if it is wanted and needed.
It means Mr Varadkar has not ruled out the much-rumoured grand coalition between Fine Gael and Fianna Fáil, but that it is not his first option.
Talks are expected to start getting more serious this week about forming a government - but no deal or indeed any sight of it is expected before the first sitting of the Dáil on Thursday.
Reporting by Sean Defoe