Fine Gael leader Enda Kenny says he has written to Waterford TD John Deasy telling him that he expects no further comment on the issue of the party's leadership before the general election.
Mr Kenny told RTÉ News the controversy of recent days had been an unnecessary distraction.
Senior Fine Gael politicians have called on all people in the party to focus their energies on winning extra seats at the general election.
The move follows demands from other party figures for a leadership contest if Fine Gael fails to get into Government.
Fine Gael's Director of Organisation and spokesman on Enterprise, Phil Hogan, said it was time for all people in the party to focus their energies on winning the extra votes necessary to win the general election.
In a statement, Mr Hogan said recent speculation regarding the leadership of the party was a non-story as the party was fully behind Enda Kenny.
He added that recent comments in the media regarding the leadership after the next election failed to recognise the reality of the party's rules and constitution.
These require that every party leader who does not lead the party into government following an election must face a vote of confidence by the parliamentary party.
Meanwhile, Fine Gael TD Michael Ring said now is not the time for a discussion on leadership.
He described challenges to the party's leadership as sabotage, but claimed he did not think it had damaged the party.
Earlier this week, former party Spokesman on Justice, John Deasy, said that if Fine Gael did not win the election, Enda Kenny would have failed and should be replaced as party leader.
Fine Gael Chief Whip Paul Kehoe said that many within the party have expressed amazement at the comments made by Mr Deasy.
Mr Kehoe said Mr Deasy's comments were not reflective of opinion within the party. He said Mr Kenny had transformed Fine Gael.
However Fine Gael TD Damien English said he believed Mr Kenny was doing a good job, but that if Fine Gael failed to win the next election, the party would have to consider electing a new leader.
Mr English said that if a new leader was to be considered he would prefer if it was someone younger.
In today's Irish Independent, Mr English was quoted as saying that when Mr Kenny was elected leader five years ago, he assumed it was for five years, unless he became Taoiseach.
Mr English is the Fine Gael Deputy Spokesperson on Justice and Community Affairs with Special Responsibility for Drugs, Alcohol and Crime Prevention.