Sinn Féin says both Enda Kenny and Attorney General Máire Whelan (pictured below) should resign - and that there should be an early recall of the Dáil next week to discuss the Fennelly Commission report.
And Fianna Fáil says it won't rule out a motion of no confidence in Mr Kenny once it has fully read the report.
The Fianna Fáil leader says the manner in which the Taoiseach presented and attempted to spin the Fennelly report was neither credible nor tenable.
But Micheál Martin's reserving judgement on whether Enda Kenny's position as Taoiseach is tenable until he reads the report fully saying the message to Martin Callinan was that he had no option but to resign.
He's also not ruling out a motion of no confidence in Enda Kenny when the Dáil returns later this month.
Sinn Féin says the Dáil should be recalled next week.
The party's Aengus O'Snodaigh (pictured below) believes Enda Kenny and the Attorney General should resign:"First of all we should have the Dáil recalled. But I think he should resign on it.
"I don’t believe his position can be taken seriously by the public.
"He is saying one thing and the Commisson of Enquiry have found against him."