Enda Kenny is to face a motion of no confidence over the findings of the Fennelly Commission.
Both Fianna Fáil and Sinn Fein say the Taoiseach's position is no longer tenable, amid claims that Enda Kenny forced the resignation of Martin Callinan to provide cover for Alan Shatter.
Micheal Martin says the Taoiseach has hidden in the past behind "fall guys" - and that with three other major players having resigned already, there is nobody left to hide behind.
He added that Kenny's decision to send a senior civil servant to Martin Callinan's home - the "immediate catalyst" for Callinan's departure" - was essentially a sacking in all but name.
Earlier the Taoiseach dismissed Fianna Fáil's criticism - saying the conclusion of the report speak for themselves.
Meanwhile there is also pressure over the role played by the attorney general, Maire Whelan, in the events that led to Callinan's departure.
Ms Whelan was the first person to brief Enda Kenny on the system of illegal Garda taping - but admitted at the time she did not have full possession of the facts of the case.
But having been told by the Taoiseach to find more information about the taping system, she decided against discuss the matter with the then-Minister for Justice, Alan Shatter - the man who would have had access to this information because of his role in overseeing the Gardaí.
Our political correspondent Gavan Reilly reports.