"Having inherited a country and an economy that was decimated by mismanagement, Enda's strong leadership and ability to make hard decisions was recognised both at home and overseas and saw our global reputation restored and strengthened", she said.
The Housing Minister says he will strive for balanced regional development if elected as Fine Gael leader and Taoiseach.
The Fine Gael leadership contest will begin on Thursday, with nominations closing on Saturday. Kenny has led the party since 2002.
As to the future Cllr Mulhall said the party has "two good candidates" in Leo Varadkar and Simon Coveney and there was talk of a third candidate.
"That landed us as local councillors in the local elections in 2014 with a hill to climb.It was tough campaign but I wouldn't blame that on Enda", he said. He is credited with leading the country out of recession and driving down the national debt, albeit with an austerity agenda that saw big cuts in welfare, health, education and policing.
British Prime Minister Theresa May and former Prime Minister David Cameron led tributes to Kenny, who was first elected as a TD in 1975. He also said he will not stand for reelection as a member of parliament.
He told a parliamentary party meeting on Wednesday that a successor would be appointed by 2 June.
Mr Varadkar now has the support of twice as numerous party's TDs and Senators as his main rival, Simon Coveney, during the first 24 hours of the race.
A number of politicians have chosen to back Coveney in this election process, including the Minister of Health, Simon Harris, and Dr. James Reilly, who has made a decision to step down from his position as deputy leader of the party.
In 2002, party leader Michael Noonan led Fine Gael to its then worst performance, losing 23 seats.
Mr Kenny will visit the Irish Cultural Centre in Hammersmith, which has been extensively redeveloped in recent years and is due to officially re-open in the coming weeks.
Among Mr Kenny's final official overseas engagements will be a two-day trade mission to Chicago and the centenary commemoration of the start of the First World War Battle of Messines.