Junior minister Jennifer Carroll MacNeill has openly admitted her ambition to become the first female taoiseach.
The Fine Gael politician had been among those rumoured to be interested in running to take over her party after Leo Varadkar's shock resignation in March.
In the end, Simon Harris was the only member to put his name forward.
Ms Carroll MacNeill, who was appointed minister of State for European affairs by Mr Harris, also hit out at the lack of women in key cabinet positions.
“We’ve never had a woman minister for Finance! We’ve never had a woman Minister for Foreign Affairs.
"We’ve never had a woman Taoiseach.
"That’s three senior positions where we haven’t had women.
"Are women not relevant to those conversations?”
On becoming leader of Fine Gael, Ms Carroll McNeill said: “I would love the opportunity to lead the country. Or to be in a leadership position.”
In an interview with
, she side-stepped a question around whether she has ever smoked marijuana."I can’t be completely responsible for everything I’ve done at four o’clock in the morning that I can’t remember!
"But I don’t ever remember smoking marijuana, put it that way. Is that a good answer?” she asked.
Addressing mounting concerns around threats to politicians, Ms Carroll MacNeill said: "What I worry about is the random attack.
"I’ve seen colleagues who have had [heated] people coming into their constituency offices, who have had things thrown at them at public events.
"We just need one of those to go too far and it becomes incredibly serious.
"And that’s what I’d be most worried about for politicians.
"Because that’s what happened in the UK with Jo Cox and David Amess.
"Both were essentially random events, but from a backdrop of increasing vitriol towards politicians generally."