Mr Varadkhar said he was pleased that Mr Coveney had chose to stay in the leadership contest, saying "it's absolutely important that we take this debate and this opportunity to reinvigorate Fine Gael to the councillors and members across the country".
Leo Varadkar was the clear favourite to succeed Enda Kenny as Ireland's Prime Minister Saturday as nominations closed for the leadership of the governing centre-right Fine Gael party.
However, Mr Varadkar performed a U-turn on his plan to retire from politics by the age of 51, saying he is now a career politician.
The Social Protection Minister will follow that up by conducting formalities at the opening of Longford-Westmeath TD Peter Burke's constituency in Mullingar on Monday evening.
Once a new party leader is chosen, members of the lower house of parliament must confirm him as prime minister, a vote likely to take place on June 13.
Last night in Tipperary, Mr Coveney told a gathering of over 300 party members that Fine Gael's best chance of making gains at the next election are outside Dublin, which is Mr Varadkar's home patch. "It's started really well and I'm really humbled at the level of support I have received from my colleagues, [but] I'm not counting my chickens".
Kylie Jenner Looks Just Like Kim Kardashian in Latest Outfit
But it was all about the eyes for once, as Kylie Jenner lounged around naked for a smoldering new photoshoot. Granted, her luxe lifestyle would be on display, but how much would we get to see the *real* Kylie.
Mr Coveney was asked by reporters if he knew which way Mr Breen and Mr Carey would vote and his response was awkward.
"I am also proposing that we consider a major change in how Ireland organises its national security services, as part of major reform of the gardai and the defence forces".
I think that is potentially a flaw in this new system that we're operating under. "I'm not going to be putting people under pressure in the spotlight of the media".
Mr Coveney did get a boost yesterday after TDs Hildegarde Naughton, Peter Fitzpatrick and Sean Barrett backed him.
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.
It remains to be seen how Tanaiste Frances Fitzgerald will vote, but sources say she will endorse her Dublin colleague.