Taoiseach Leo Varadkar said allowing Fianna Fáil back into power would be like letting John Delaney run the Football Association of Ireland (FAI) in nine years' time.
Mr Varadkar compared Fianna Fáil to the controversial football chief during a televised debate on RTÉ's 'Prime Time'.
During a debate on the economy, Fianna Fáil leader Micheál Martin said Sinn Féin's economic plans were based on "magic" money coming from a fairy tree.
Mr Martin said people would be "taxed out of existence" under Sinn Féin's financial plans and said this would lead to investment leaving Ireland.
Sinn Féin leader Mary Lou McDonald said the "political establishment" would find every reason in the world to provide breaks and reliefs to big corporate entities.
She accused Mr Martin of trying to "mansplain" the economy to her when he criticised her party's tax plans.
Mr Varadkar interjected to compare Fianna Fáil to the former FAI chief executive.
The Taoiseach also criticised Ms McDonald over the homeless figures in Northern Ireland where Sinn Féin has been in power for more than two decades.
Mr Varadkar said the official statistics show there are 20,000 people homeless in the North, which is more than in this State where it has hovered at around 10,000.
He also said hospital waiting lists in the North were longer and suicide rates were three times higher.
Ms McDonald said: "I'm sure somebody will factcheck that figure and find that it's wrong."
She said London controlled the "purse strings" in the North and there had been a decade of "Tory austerity".
Separately, Ms McDonald repeatedly refused to give her personal view on the Special Criminal Court which is responsible for convicting serious criminals and terrorists.
Ms McDonald was asked her opinion on the court several times during the debate.
She said she was in favour of courts generally, but would not directly address the Special Criminal Court which her party previously said should be abolished.
The court has successfully convicted members of the Provisional IRA.
She said Sinn Féin was now seeking a review of the court, which would be led by a High Court judge.
However, she repeatedly refused to answer questions about her own views on the court when posed by hosts Miriam O'Callaghan and David McCullagh.
Mr Varadkar said he was ruling out any coalition with Sinn Féin because of its view on the Special Criminal Court.
He said he was concerned about the party's past but also concerned about its present views on the court.
Mr Varadkar said Sinn Féin was against the Special Criminal Court, which he said locks up "garda killers" and serious criminals such as members of the Kinahan crime gang.
He said Ms McDonald was not giving a straight answer on the question because she did not want people to know her views.
Mr Martin said Sinn Féin always voted against the Offences Against the State Act, which legislates for the Special Criminal Court.
He said Sinn Féin voted against the act because it was being told to by its "IRA comrades".
Meanwhile, Mr Varadkar defended Fine Gael's record on health and claimed it was only in the past two years that the Government had balanced the books and was able to spend more on the health service. "I don't think it's right to say that we've had nine years," he said.
Ms McDonald said the new national children's hospital was the most expensive in the world at €1.4bn.