Therefore I will retire as Leader of Fine Gael effective from midnight tonight, 17th May 2017.
"He would be a quite capable of leading the party and the other man Leo Varadkar would as well.but I would be sticking my neck out and saying I would be supporting Coveney", he said.
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.
"And also devolving a new social contract".
When asked about comments Mr Varadkar made in 2015 that he would stay in politics for another 15 years, he said he was not sticking to that timeline.
Louth Deputy Peter Fitzpatrick, meanwhile, has announced he will vote for Simon Coveney.
"While over the years we have had our differences on many political and policy issues, I have always appreciated Enda's decency, good humour and approachability", he said.
BoyleSports can report support for Simon Coveney on Thursday morning and as a result, the Cork native is now 6/4 from 7/4 to be the new Fine Gael leader.More news: National Safe Boating Week 2017 stresses life jackets
"He took the tough decisions and because of those the decisions the country is back to where we are today", she commented.
But Minister Coveney says despite this the campaign isn't over yet.
In his statement Mr Kenny said he will remain as Taoiseach until June 2nd.
Minister for Foreign Affairs Charlie Flanagan, meanwhile, declared his intention to support Mr Varadkar saying he was the "change candidate".
He has been under growing internal party pressure over his failure to secure a majority government in the general election in 2016 and his handling of a series of crises in the Irish police.
The two frontrunners to succeed Mr Kenny - Simon Coveney and Leo Varadkar - also paid tribute. He has a very tough job at the moment as Minister for Housing.
The Cork South Central TD, who is now the Minister for Housing, Planning, Community and Local Government, is expected to contest the election to become leader of the Fine Gael party with the Minister for Social Protection, Leo Varadkar; an announcement is expected from Minister Varadkar later today.
Varadkar - who will not officially launch his campaign until tomorrow - appeared in public for the first time since the leadership election got underway.