Fianna Fáil TD Darragh O'Brien has said the "vast majority" of Fianna Fáil parliamentary party members support Micheál Martin and that the fallout from the Presidential Election does not signal the beginning of the end for the party leader.
It comes as Fianna Fáil Cork East TD James O'Connor said that everything, including a change of leader, must be up for discussion, echoing calls made yesterday by Fianna Fáil TDs John McGuinness and John Lahart.
Speaking on RTÉ's Morning Ireland, the Minister for Transport said that Mr Martin was an "exceptional leader".
"If you look at the 14 years that Micheál Martin has led Fianna Fáil, he's brought the party back, literally, from the brink, back to be the largest party in Government," he said.
"He has shown great leadership over the course of that, in relation to referenda that we've had in relation to same-sex marriage, in relation to women's reproductive rights and Repeal the 8th.
"Micheál has actually been an exceptional leader, who's been brave in what he has done and has led the party with distinction."
Mr O’Brien said that the "vast majority" of parliamentary party members support Mr Martin, despite indications that ten of the required 12 signatures for a no confidence motion in Mr Martin have been secured.
"We have 48 TDs, we have over 20 senators in the parliamentary party as well. The vast majority of them support Micheál Martin as leader unquestionably," he said.
"We're in politics to represent our people, represent our constituencies, and the Presidential Election did not work out for us. Learnings need to be made and will be made from that.
"But I think if you look back, to be fair to the party leader, over the last 14 years, he's got all of the big calls right in that period of time. This was something that we will unquestionably, as professional politicians, reflect upon, learn from, and make sure it doesn't happen again."
With Mr Martin approaching 15 years as party leader, Mr O’Brien said it was too early to say if there were concerns over Mr Martin’s leadership ahead of the next general election.
"Micheál Martin has been written off many times and actually, Fianna Fáil has been written off many times, over the period of 14, 15 years," he said.
"The next national elections are nearly four years away. I wouldn't be reading into too much on this election as to how that would actually affect an election that's three, four years away."
Backbench TDs 'fed up' with not being listened to by party leadership - Byrne
Fianna Fáil TD Malcolm Byrne has said the party's backbench TDs are "fed up" with not being listened to by senior party leaders and "need to take control back".
Speaking on RTÉ’s News At One, the Wicklow-Wexford deputy said he has "enormous respect" for party leader Micheál Martin, but Fianna Fáil’s issues run deeper than "the disaster that was the Presidential Election".
"We're not seeing delivery quickly enough on some of those key issues and part of it is, I think, that frankly, we as elected representatives are fed up and part of it is our own responsibility.
"But that you have a situation whereby you have state agencies that have taken on so much power who are not delivering.
"We've been trying to communicate this, but we feel that we're not being listened to at senior levels within the party," Mr Byrne said.
'Huge annoyance' in FF over Áras election - Rabbitte
Meanwhile, Fianna Fáil Senator Anne Rabbitte has said there is "huge annoyance" within Fianna Fáil regarding the party’s handling of the Presidential Election.
Speaking to RTÉ’s Morning Ireland, Ms Rabbitte said the issue is "far deeper" than the ongoing party review into the presidential campaign.
"I think its far deeper than that now, that’s the feedback I’m getting from the grassroots, that’s the feedback I’m getting from the councillors. There’s huge annoyance about the last 24 hours."
Yesterday, a decision was made by those unhappy with party leader Micheál Martin to allow the review of the party's presidential campaign to be completed within the next fortnight before any action is taken.
Sources close to the party leader said a party review of the presidential campaign is well under way and will be completed within weeks.
Cork East TD James O'Connor said the internal review of the presidential campaign must ensure that such mistakes are never repeated.
Mr O'Connor said he has not been told how he can contribute to this review.
A former TD for Galway East, Ms Rabbitte said that there is "a huge amount of annoyance and upset" among Fianna Fáil members in Galway.
"There is a conversation that needs to be had to move it forward, in relation to how we got it so wrong," she said.
Ms Rabbitte said that the question of Micheál Martin’s leadership will be up to the Fianna Fáil parliamentary party members.
She said she agreed with Fianna Fáil TDs John Lahart and John McGuinness, who spoke yesterday regarding Mr Martin's leadership.
Watch: Lahart says Presidential Election result reflects error of judgement that will have consequences
Mr McGuinness said that the party needs a new leader in the not too distant future.
"We do have to look at the structures within the party, but we also have to question the leadership team, which is made up of the Taoiseach, some unelected advisers and Fianna Fail headquarters," he said.
Speaking on RTÉ's This Week, he said the party made "serious errors" in the Presidential Election campaign, which ultimately saw its candidate Jim Gavin dropping out of contention.
Mr Lahart said members of the parliamentary party were actively talking about Mr Martin's leadership.
"It is a conversation that the party needs to have. The events of the last few weeks, the result yesterday, and the outcome of the result have brought that conversation forward," Mr Lahart said.
Mr Lahart said the centre has not held politically and a left-right divide has been created in Irish politics for the first time.
"I don't think Fianna Fáil can just sit back and observe that," he said.