Taoiseach Enda Kenny has claimed Fianna Fail are not fit for government and Micheal Martin has "isolated" his party from that possibility.
In the first real fighting talk of the election campaign, the two party leaders traded blows over who should be the next Taoiseach.
During a radio interview, the Fianna Fail leader said people want Enda Kenny out of office and that Fine Gael's right-wing policy for reducing tax would damage public services.
He also insisted he can lead the next government despite his party lagging behind Fine Gael and Sinn Fein in the polls.
But responding from the Netherlands, where he is on a trade mission, Mr Kenny said the attack was an act of "desperation".
"They've already isolated themselves completely from government and that's in the words of Micheal Martin himself.
"Here's the leader of a party, the direct link to what caused an economic catastrophe in our country, which drove away thousands of our young people," the Taoiseach said.
He argued that Mr Martin "wants to return back to the ways that drove those people away".
And he suggested Fianna Fail are now "convulsed" with attacking Fine Gael in an effort to distract from their battle with Sinn Fein.
Mr Martin then issued a statement through the press office accusing Mr Kenny of resorting to "a string of well-worn cliches".
"No matter how much he blusters, Enda Kenny can't get away from the fact that his tax plans are deeply unfair," Mr Martin said.
Sinn Fein leader Gerry Adams also weighed into the argument accusing both politicians of engaging in a "sham fight".
"The present Fine Gael-led Government is merely implementing a policy plan laid out for it by their Fianna Fail predecessors," he said.