Taoiseach Enda Kenny has dismissed calls for him to resign early.
After Fine Gael backbencher Brendan Griffin broke ranks and demanded a new leader by September, Mr Kenny insisted he has a mandate and job to complete.
The Taoiseach previously said he would serve a full term in office but not lead his party into the next election.
At an event at the Sacred Heart Hospital and care home in Castlebar, Co Mayo, Mr Kenny ruled out an early departure and said his focus has always been on securing Ireland's future.
"I have no intention of being diverted from that work that I have undertaken, and for which I have received a mandate to fulfil," he said.
"That's my focus and my focus is entirely on the future.
"For those who might be interested, I will not be diverted from that task and that duty and that responsibility which is the mandate given to me by the people."
Health Minister Simon Harris, Education Minister Richard Bruton and Foreign Affairs Minister Charlie Flanagan have all ruled out supporting a leadership heave.
Questions over Mr Kenny's future were sparked by Kerry TD Mr Griffin, who said a new leader would be the only way to stop Fianna Fail forcing another election in the autumn.
He also refused to rule out pushing for a vote of no confidence in Mr Kenny.
Fianna Fail agreed to support the Fine Gael minority government for three budgets but Mr Griffin said his counterparts cannot be trusted not to use budget decisions as an excuse to force another general election.
Mr Kenny is in Germany tomorrow for talks with Chancellor Angela Merkel.
One of the key issues is Brexit with the Taoiseach warning that Ireland is facing a major challenge by the UK's planned break with the European Union.