Jokes about Kenny also fall flat at Fine Gael's annual think-in
Mr Varadkar poked fun at his former leadership rival Foreign Affairs Minister Simon Coveney who was noticeably unimpressed by the comments made in front of the media and the Fine Gael parliamentary party.
Mr Varadkar also joked that former Taoiseach Enda Kenny's Ard Fheis speeches had been "iffy" and made fun of Mr Coveney's supporters.
After the meal, Mr Coveney is understood to have told colleagues he did not think Mr Varadkar's jokes about Mr Kenny were appropriate.
The minister's views were shared by other TDs who said they felt comments about the former Taoiseach and the current Fine Gael deputy leader were "disrespectful".
Sources close to the Taoiseach insisted that all his comments were intended to be "good natured" and not meant to offend anyone. At the event in Clonmel, Tipperary, Mr Varadkar delivered an American-style 'roast' speech similar to those used by US presidents to make fun of Washington correspondents. The Taoiseach told the audience that he had contacted Mr Kenny to ask him for advice on making his first after-dinner speech at a Fine Gael think-in.
"I said you've done about 15 now of these after-dinner speeches and you do them very well. Ard Fheis speeches were a bit iffy (but) I didn't say that," Mr Varadkar said.
He also joked that he couldn't have a drink before making the speech thanks to "Dr Brian Cowen" and Mr Coveney. In 2010 Mr Coveney controversially said Mr Cowen "sounded half way between drunk or hungover" while been interviewed on RTE Radio One's Morning Ireland after a Fianna Fail think-in.
Mr Varadkar also joked that "so many people from the Rebel County" voted for him in the leadership election because Cork had never won an All Ireland under a Cork Taoiseach.