Simon Coveney has refused to concede the day-old battle to be the next taoiseach.
As Leo Varadkar, his only rival for the leadership of Fine Gael, became the early frontrunner with strong support from cabinet and backbench colleagues, the Housing Minister said he was not panicked.
Mr Coveney dismissed the idea of cutting short the contest and said he has never lost an election.
“They’ve got an early head start, there’s no doubt about that,” he told Clare FM. “We are not panicked by that in any way.”
In what is expected to be a two-horse race, almost 21,000 Fine Gael party members will vote at 26 polling stations from May 29 to June 1, and the parliamentary party, which includes 73 TDs, senators and MEPs, will vote in Dublin on June 2.
The contest is decided by an electoral college, with the parliamentary party worth 65% of the total vote, rank-and-file members accounting for 25% and 235 local representatives making up the remaining 10% of the vote.
The winner will be announced in Dublin on June 2.
About 20 members of the Fine Gael parliamentary party have yet to declare for one side, with Social Protection Minister Mr Varadkar having about twice as much support from that section of the party.
He was humbled by the early support he secured but insisted the contest was not over.
“I’m really humbled, really grateful for that,” he said.
Mr Varadkar has an apparent strong lead over Mr Coveney, with the backing of Paschal Donohoe, Minister for Public Expenditure and Reform, Foreign Affairs Minister Charlie Flanagan and Education Minister Richard Bruton among others.
Mr Coveney has supporters including Health Minister Simon Harris and Senator James Reilly.
Mr Varadkar said it had been his idea originally to extend voting rights for the leadership of Fine Gael to all the party’s elected representatives.
Setting out his stall, he said: “I want to take the country forward. We’ve been through a really difficult recession which is now over but the wounds caused by the recession are still real and many of them are open. We are now at a crossroads, in my view.
“We can repeat the mistakes of the past, allow ourselves to lose control of public spending, fuel the property market … or this time we can get it right.”
Candidates for the Fine Gael leadership have been warned to sign up to a code of conduct to govern their behaviour in the campaign and they are also obliged to abide by data protection rules governing the use of membership details.
Nominations close on Saturday evening and with the contest appearing to be down to two men, four hustings have been planned for Dublin, Carlow, Ballinasloe and Cork over four nights from next Thursday.