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". The focus will now turn to a number of Ministers who have yet to outline whom they will support.
He added: "Most importantly, I want to take the country forward".
Speaking for the first time since the contest was announced, Mr Varadkar said he was not "counting his chickens yet".
He said the county would be a priority for him should he become Taoiseach.
Mr Varadkar, the social protection minister, is one of two front-runners to succeed Mr Kenny.
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Mr Donohoe stated his intention to vote for Mr Varadkar in an interview on RTÉ's Morning Ireland.
Sinn Féin president Gerry Adams said Mr Kenny "did his best from his perspective" but his "political legacy is dominated by crisis, chaos, and chronic lack of accountability".
No formal announcement was made despite rumours to the contrary that party strategists were looking at dates in the second and third week of June.
In a statement he says he has learned a lot from Enda and his legacy will be far-reaching. "That is precisely what we need right now and I believe Simon Coveney will deliver on this", Mr Harris said.
Mr Donohoe said it is a matter for the next taoiseach whether he would have a Cabinet role, refusing to say whether he would seek the role of Minister for Finance. Rank-and-file members are given more voting strength than councillors, but substantially less than the parliamentary party.
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"I think he can connect much closer with an electorate who may not be Fine Gael", said the former TD.
While Mr Varadkar is expected to personally launch his bid on Saturday, Mr Coveney fired the opening salvo on the steps of his party headquarters and declared he was not going to engage in sound bites and glib put-downs. He has a very tough job at the moment as Minister for Housing.
Other achievements during the 66-year-old's time in government include the legalisation of gay marriage.
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.
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US officials expressed their displeasure with the presence of Bashir at the summit and urged the host country to not invite him. Saudi Arabia is not a signatory to the statute that founded the ICC and neither Sudan nor the USA have ratified it.
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