A Fine Gael backbencher says the party needs a new leader by September.
Brendan Griffin says the past fortnight has shown Fine Gael is "rudderless" and completely unprepared for an election.
Speaking to Radio Kerry, Deputy Griffin says Enda Kenny needs to allow an orderly succession process take place.
Mr Griggin said: "We've a Taoiseach who says he wants to serve a full term and a Taoiseach who says he doesn't want to lead us into the next General Election.
"Those two positions are incompatible and as a result it is leading to huge uncertainty and a lack of stability and that's what needs to be addressed.
"We are rudderless as a government, particularly as the last fortnight has shown how vulnerable and precarious the Government is."