Simon Harris is set to become the next Fine Gael leader and Taoiseach.
The Higher Education Minister looks increasingly likely to be unopposed in his bid to replace Leo Varadkar.
The 37-year-old has been in an almost unassailable position since he became the first candidate to secure enough backing for a nomination this morning.
In the hours since, his rivals for the leadership have backed away one by one.
After first refusing to say whether he was entering the race, Public Expenditure Minister Paschal Donohoe confirmed that he had decided to opt out.
"I have long said that my focus is on the two jobs that I am privileged to hold - that of Government Minister and as President of the Eurogroup," he said in a statement.
"That remains to be the case. It is with a huge honour that I undertake my work on the domestic and international stage.
"I do believe that a wealth of talent and experience exists in Fine Gael and that exciting times lie ahead, both for the Party and ultimately for the country," he added.
On Lunchtime Live meanwhile, Justice Minister Helen McEntee confirmed that she was throwing her support behind Minister Harris.
“I will be supporting him and wish him every success and, indeed, anybody who puts themselves forward,” she said.
“I’ve been very clear this morning that I thought there should be a competition and I think it’s good for people to see a competition within a part.
Speaking to Newstalk outside Government Buildings shortly later, the Social Protection Minister Heather Humphreys also ruled herself and said she was endorsing Minister Harris.
"I have thought about it and given it very serious consideration and I've decided not to put my name forward," she said.
"But I have decided to give Simon Harris my full support," she added.
Enterprise Minister Simon Coveney, who previously lost the Fine Gael leadership race to Mr Varadkar, ruled himself out of the running last night.
It leaves Minister Harris with no clear rival for the position – although he has yet to officially announce his candidacy.
Candidates need the backing of at least six members of Fine Gael's Parliamentary Party with voting taking place in early April.
If he is elected leader a vote would then be held in the Dáil, during which Minister Harris would require the support of the coalition partners Fianna Fáil and the Green Party.
It comes as Taoiseach Leo Varadkar is attending his final meeting of EU leaders in Brussels before he steps down next month.
Mr Varadkar has insisted that “no one thing or event” pushed him to announce his resignation.
Speaking in Brussels this morning, he said he was moving on to “make space for new people, new ideas and new energy”.