Health Minister Simon Harris and Tánaiste Frances Fitzgerald have joined Richard Bruton in failing to rule themselves out of the running to be the next Fine Gael leader.
Mr Harris went as far as to list his leadership credentials while insisting there was "no vacancy" for the job.
Cabinet members and TDs await Taoiseach Enda Kenny's expected statement on his future to the Fine Gael parliamentary party tomorrow.
While Leo Varadkar and Simon Coveney have long been viewed as best-placed ministers to succeed Mr Kenny, a compromise candidate remains a distinct possibility.
Mr Harris twice yesterday declined to rule out his name going forward as a possible candidate.
On the second occasion, during a visit to University Hospital Galway last night, Mr Harris (30) indicated that youth shouldn't be a barrier to consideration for the job.
"Age to me is immaterial, I look to be judged on my job and the job that I am doing, and I am working as hard as I possibly can at that job," he said.
Mr Harris added: "I try to provide leadership in whatever role I am given", listing his time as a county councillor, TD and previous role as junior minister.
"There is no vacancy in the Fine Gael party. If and when one does arise I will consult with colleagues at that point," he said.
Earlier, he insisted he was dedicated to his job as Health Minister.
He was responding to a WhatsApp message from Foreign Affairs Minister Charlie Flanagan posted in a Fine Gael chat saying: "He hasn't announced yet but Frances is encouraging him. He wants out of Health."
Mr Harris said: "My colleague Charlie Flanagan has many, many fine attributes. He's a great colleague of mine but I think funny jokes on a Sunday afternoon is clearly not one of them.
"I'm absolutely honoured to hold this position."
The message was dismissed as "jovial Sunday afternoon banter" by Mr Flanagan, who also said: "I regret that it's been taken so seriously."
Ms Fitzgerald has also left the prospect of a bid for the leadership open.
"It's very important that we wait and hear what the Taoiseach has to say [on Wednesday]. And when he's made that clear I'll be considering my own position," she said.
Meanwhile, the Education Minister, who launched an unsuccessful heave against Mr Kenny in 2010, again failed to rule out a bid, having previously declined to do so last Friday.
He said: "There is no vacancy. I'm not commenting on any of the contenders, I'm not commenting on this matter."
Mr Bruton said the country faced challenges, including Brexit and political change in the US.
"This is a time of challenge and we as a mature party need to sit down together, discuss the issues and make the right decisions for the future and that's my primary interest," Mr Bruton said.
Taoiseach Enda Kenny last Thursday insisted he's focused on his work and a series of engagements in the coming weeks. He said: "I'm focusing entirely on a really busy and challenging time ahead. Politics is a vocation. It draws you into stormy waters as well as calm."
Health Minister Simon Harris has listed the credentials which would make him an ideal candidate to take over as leader of Fine Gael and he has dismissed any suggestion that he would be too young to take charge if the opportunity arose.