Micheal Martin has accused Mary-Lou McDonald of having a sense of entitlement to power.
He claimed the Sinn Fein president’s address to her party ard fheis on Saturday evening lacked substance.
The Fianna Fail leader told RTE’s This Week it was a flat speech.
He said: “There was no radical proposals or solutions contained within the speech.
“And there was a sense of entitlement, that somehow Fianna Fail or Fine Gael owed Sinn Fein power.
“And I think what is revealing in the last week and revealing from Mary-Lou McDonald’s speech is this sense that Sinn Fein and Fine Gael are all talking about power, getting into power, and not focusing on the key issues and the key challenges facing the people of the country.”
Ms McDonald addressed a range of matters, including homelessness, hospital waiting lists and the cervical smear check controversy.
Sinn Fein has decided not to table a motion of no confidence in Housing Minister Eoghan Murphy before the Dail summer recess.
Fianna Fail’s confidence and supply arrangement with Fine Gael underpinning the minority Government is nearing the end of its originally agreed period.
It effectively runs out after the October budget.
On Saturday, Ms McDonald said her party would not be excluded from Government by Mr Martin or Leo Varadkar.
She said it was no longer “their way or the highway” and it was up to the people to decide.
Mr Martin told RTE he still harboured concerns about how Sinn Fein operated despite the change in leadership.
He added: “Just because you change the podium, you don’t change the party.”