The Cork South Central TD said his fellow Corkman was doing an “excellent job” in bringing about a modest recovery of the party.
Mr McGrath rejected what he described as “silly season” reports of dissatisfaction with the leader among the front bench and, furthermore, speculation he would launch a challenge before the next general election.
“No one has approached me from the parliamentary party expressing unease about the leadership,” Mr McGrath told the Irish Examiner.
Asked if he has any plans to mount a leadership challenge, he said: “Absolutely not. I have no idea where that story is coming from. Micheál Martin is doing a very good job as leader of the party and I don’t see any reason why his leadership would be under any threat.
“I certainly have no plans whatsoever in relation to the leadership.”
Mr McGrath did not rule out the possibility of some day leading the party, but added: “I don’t think the issue is going to arise for a good number of years.”
He said it was “unfair to the incumbent for anyone to express ambitions to be leader in the future”, but that “we’ll cross that bridge when we come to it”.
Mr Martin has been leader of Fianna Fáil since Jan 2011 and is steadily rebuilding its support from just 17% in the last election to 29% in the latest opinion poll. There are concerns that his membership of Brian Cowen’s cabinet during the bank bailout and the arrival of the IMF could be a liability.
His leadership suffered its first significant setback when he failed to reach consensus among his TDs and Senators to support the Protection of Life during Pregnancy Bill. He allowed a free vote and six TDs, including Mr McGrath, went against his wishes and opposed the bill.
Mr McGrath said that is all “water under the bridge at this stage” and that Mr Martin did the right thing by allowing a free vote, because the majority of the parliamentary party voted against it.
“He has done an excellent job over the last year or so. The party is on the road to recovery, be it a modest recovery. A lot of work has been done reforming the organisation, empowering the membership, and a platform is there for the recovery of the party,” he said.
Meanwhile, Roisín Shortall, the former junior minister, has been holding talks with a number of other former Labour TDs and Independents about forming a new left-wing Dáil group.
John Halligan, Thomas Pringle, and Catherine Murphy are among those expected to join four former Labour TDs in the new group in September.