Irish Taoiseach (Prime Minister) and Fine Gael (United Ireland Party) leader Enda Kenny said Wednesday he will retire as the party leader effective from Wednesday midnight.
But at a parliamentary election a year ago, Fine Gael suffered a backlash from voters who felt the recovery was passing them by.
Her predecessor David Cameron said Mr Kenny "was a strong leader for Ireland, a great partner for the United Kingdom, and remains a good friend".
"He did his country much service, and I wish him the very best in the next chapter of his life".
Earlier, Paul Keogh TD has also said that he will support Mr Varadkar.More news: ICC Champions Trophy: Raina, Gambhir dropped again as Rohit, Shami make cut
Mr Kenny paid tribute to loyal constituents and supporters in Mayo who he has represented since 1975 and to his personal staff.
Both are expected to announce their candidacy on Thursday.
I have chose to implement that decision today.
The announcement came a day after Kenny said he would quit, kicking off a succession contest that was confirmed as a race between two younger ministers after other potential candidates stepped aside and colleagues began to pick sides.
Helen McEntee, another junior minister in Mr Varadkar's camp, said: "Look at the fresh new approach he has taken to politics, look at how he interacts with people, look at his vision for a more forward-thinking and open Ireland".More news: Always Dreaming a 4-5 favourite entering Preakness
Ministers Charlie Flanagan and Paul Kehoe, as well as TD Fergus O'Dowd, have also backed Varadkar.
Based on yesterday's and today's declarations, Mr Varadkar has established a lead within the parliamentary party but those campaigning for Minister for Housing Mr Coveney say a significant number remain undecided.
Fianna Fail's Michael Martin is the current 1/2 favourite to be Taoiseach after the next general election with Leo Varadkar next at 9/4 and Simon Coveney priced at 6/1.
"Believe it or not it was my proposal back in the late 90s that we should extend the vote of FG leader to members and councillors".
Kenny has been prime minister of Ireland since 2011, and has led Fine Gael for the past 15 years.More news: Brazil's Temer: 'I won't resign' amid corruption allegations
"[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".
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