Enda Kenny has been asked to reconsider the appointment of James Reilly as deputy leader.
The calls have come at the weekly meeting of party TDs and Senators, with one TD threatening to force a vote on Reilly's appointment.
The Taoiseach is said to have got a strong round of applause as he finished addressing the weekly Fine Gael parliamentary party meeting in Leinster House this evening.
But four TDs have openly questioned his decision to reappoint James Reilly as Deputy Leader, despite losing his seat in the Dáil.
Our political correspondent Gavan Reilly reports: