Deputy Fitzpatrick has said that he would be backing the current Housing Minister to succeed Enda Kenny as party leader and Taoiseach, describing him on local radio as "the whole package".
Prime minister since 2011 and leader of his party for nearly 15 years, Kenny is expected to be replaced by either Social Protection Minister Leo Varadkar, 38, the bookmakers' favorite, or Housing Minister Simon Coveney, 44.
He told his party he would remain as leader for a "brief but appropriate period" to facilitate a leadership contest.
Flanked by Paschal Donohoe he arrived with cupcakes and coffees for the media gathered in Dublin.
He has led the centre-right Fine Gael party for 15 years and been prime minister since 2011.
Dubliner Leo Varadkar remains the odds on favourite to get the job but following the support for Coveney, he has been eased to 8/15 from 2/5.
Fianna Fail leader Micheal Martin said Kenny had worked diligently for his country over many years.
He said that like any politicians, Mr Kenny had "his highs and lows" but he praised general his performance over two governments.
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".
"I'm really humbled, really grateful for that", he said.
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Just a few minutes later, Smart took the same walk and smiled at Olynyk - already sitting in his auto and waiting to go home. John Wall wasn't much help either, finishing with 18 points on 8-of-23 shooting and disappearing late in the game.
His departure has been long anticipated after the party returned to power past year in a fragile minority coalition, which is dependent on the support of the opposition party Fianna Fail.
Paul Kehoe argued: "As the political landscape continues to shift, at home and overseas, his forthright style and ability to effect change, makes him the best placed candidate to deal with the challenges facing us".
Junior minister Paul Kehoe also backed Mr Varadkar, Ireland's first openly gay cabinet member.
Kenny said Fine Gael would name his successor no later than June 2.
In a statement on his way into a parliamentary party meeting on Wednesday evening, Kenny said he would continue as prime minister pending the election of his successor.
The contest will be decided using a weighted voting system across three electoral colleges - the parliamentary party, councillors and party members.
No one deserves it more.
Sarah Bardon from the Irish Times political staff stressed that the race is not over yet.
David Cameron took to Twitter to pay tribute, posting: "Enda Kenny TD was a strong leader for Ireland, a great partner for the United Kingdom, and remains a good friend".
The regional debates, or hustings, will take place in Ballinasloe, Dublin, Carlow and Cork over four days next week.