Tánaiste and Minister for Finance Brian Cowen is now almost certain to be elected as the next Fianna Fáil leader when nominations for the post close on Saturday afternoon.
This follows the announcement this evening by the Minister for Transport Noel Dempsey that he would support Mr Cowen's leadership bid.
Mr Dempsey was the only realistic candidate left who could have opposed Mr Cowen.
Earlier Minister for Arts, Sport and Tourism Séamus Brennan also declared his intention not to run for the post, saying his decision was in recognition of the Mr Cowen's work for the Government and the party.
Mr Brennan's move followed a similar declaration from Minister for Foreign Affairs Dermot Ahern.
Mr Ahern said he had made up his mind some time ago not to enter the leadership race and that he would support Mr Cowen's bid.
Throughout the day ministers expressed their support for Mr Cowen and declared they would not be entering the race.
Nominations for the post of leader close on Saturday at 2pm and a meeting of the parliamentary party scheduled for Wednesday next will then elect a new leader.
Mr Cowen, who is a hugely popular figure in the party, would probably prefer to win a contest to add legitimacy to his position rather than be elected unopposed.
But all likely opponents have declined the opportunity to mount a leadership challenge.
Minister for Justice Brian Lenihan and Minster for Enterprise, Trade and Employment Micheál Martin ruled themselves out yesterday and early this morning respectively.
"In my view there's not a necessity for an election," Mr Martin said. "But again other candidates may come forward, other people may have different perspectives.
"I think it's very much a matter for them, it would be their entitlement and I don't want, in anyway, to suggest that people shouldn't," Mr Martin told RTÉ this morning.
He was among four ministers who have pledged their support for Mr Cowen. Minister for Education Mary Hanafin, Minister for Defence Willie O'Dea and Minister for Social and Family Affairs Martin Cullen are the others.
Ms Hanafin said today Mr Cowen "had the full backing of the parliamentary party".
Mr Cullen said the Laois-Offaly TD, who is also Fianna Fáil deputy leader, was "head and shoulders" above other prospective candidates.
"I think he was an outstanding force for Fianna Fáil and indeed stability for the country in economic terms as minister for finance during the last general election ... I've no doubt in my mind that if Brian Cowen puts his name forward he will certainly have my full support," he told Newstalk this morning.
Minister of State for European Affairs Dick Roche declared his support for Mr Cowen, describing him as "without doubt the brightest mind in Dail".
The expressions of public support for Mr Cowen made it more difficult for Mr Ahern, who was at one stage his most likely challenger, to enter the race. He said this afternoon that he had decided yesterday not to enter the race and had told Mr Cowen of his intention to support him.
This means Mr Cowen will now likely lead the party in the Reform Treaty referendum likely to be held in the second week of June.
In order to become Taoiseach he must elected by members of the Dáil first.
Fine Gael leader Enda Kenny yesterday called for a general election to be called to ensure the new Fianna Fáil leader had a mandate to govern. However, it is more likely that the Coalition would support the new Fianna Fáil leader's nomination for Taoiseach.