More members of the parliamentary party have been announcing endorsements
The Government Chief Whip Regina Doherty is laying her support behind Leo Varadkar in the Fine Gael leadership race.
Ms Doherty says Mr Varadkar 'has the smarts, integrity and sincerity' for the job.
In a statement, she says: "I want Fine Gael policies to reflect the values of our membership. I want Fine Gael policies to provide solutions to the challenges that the Irish people face.
"Fine Gael has built a strong reputation for our management of the Irish economy from near collapse to renewed strength.
"I believe that Leo Varadkar will be fearless in seeking to deliver a social recovery alongside that.
"For me he is the most impressive politician of my generation."
Both candidates insist the campaign is far from over, despite Mr Varadkar having a significant lead over rival Simon Coveney.
The housing minister earlier told Clare FM he is not worried about the lead by the social protection minister.
"For me, politics is about changing Ireland for the better.
"It's not about press releases, it's not about media star quality and so on.
"It's about having a real plan that can impact on people's lives, about upfront intelligent and honest about how you're going to actually make that happen.
"And that is what I'm about in politics".
Mr Varadkar - who will not officially launch his campaign until Saturday - appeared in public for the first time since the leadership election got underway.
He posed for photographs on Leo Street in Dublin with Minister Paschal Donohoe, and confirmed the worst kept secret in Irish politics: "Today I want to confirm that I will be a candidate for the Fine Gael leadership vacancy."
"I believe that I can modernise and transform Fine Gael, make it a campaigning party and a fighting force again.
"[I want] to open a conversation with people who don't support us, people who've lost faith in us, or people who've maybe never considered voting for Fine Gael."
He added: "Most importantly, I want to take the country forward."
The two candidates have also launched campaign videos.
Speaking on Newstalk Breakfast earlier, Public Expenditure Minister Paschal Donohoe described Mr Varadkar as "the most substantial and capable politician of my generation".
Minister Donohoe explained: "He has a rare combination of intellect and judgement that I believe make him the best person to lead Ireland as we deal with new risks, and make the most of some great opportunities."
He said he made the decision on the back of his experiences dealing with the two men over several years in Cabinet.
He explained: "It's the track record of how I've seen each of them perform across that period... I hold Simon in great esteem, but it's how I have seen Leo respond back to great need is why I'm supporting him.
"I saw firsthand his moral compass in relation to looking to make sure all who are vulnerable and depend on our social welfare system could receive a set of additional supports in last year's budget. He fought tenaciously for that - not for any political reason, but because he believed it was the right thing to do."
Ministers Charlie Flanagan and Paul Kehoe, as well as TD Fergus O'Dowd, have also backed Mr Varadkar.
Paul Kehoe argued: "As the political landscape continues to shift , at home and abroad, his forthright style and ability to effect change, makes him the best placed candidate to deal with the challenges facing us."
Louth Deputy Peter Fitzpatrick, meanwhile, has announced he will vote for Simon Coveney.
Minister Dara Murphy suggested that Mr Coveney has the qualities needed to lead Ireland.
The Cork North Central TD is backing his fellow Cork man to take over as leader of the Fine Gael party and Taoiseach.
Speaking to Cork's 96 FM News, the Minister for European Affairs said: "I've worked and known Simon Coveney for many years, and I think he's got the qualities we need at this time to lead the country."
Other members of the parliamentary party have signaled they too will make their intentions known.
Last night, it was decided that nominations will close tomorrow evening - but it is not believed that any other candidates will enter the race.
Sarah Bardon from the Irish Times political staff stressed that the race is not over yet.
Meanwhile, the party has revealed details of how Enda Kenny's successor will be chosen - with the party using an electoral college system for the first time.
From Thursday to Sunday next week, there will be four regional debates or hustings - in Dublin, Carlow, Ballinasloe and Cork.
Between Monday May 26th and Thursday June 1st, voting for 235 councillors and up to 21,000 members will take place at 26 polling stations across the country.
On Friday June 2nd, TDs, senators and MEPs will vote. All the votes will then be counted, and the winner announced.