Both Fianna Fáil and Sinn Féin say they will both be bringing forward motions of no confidence in the Taoiseach Enda Kenny.
Fianna Fáíl say they are tabling a motion of no confidence in Mr Kenny over his conduct in relation to the resignation of former Garda Commissioner Martin Callinan when the Dáil resumes.
While Sinn Féin say they too will introduce a motion of no confidence in the Taoiseach and the government "at the earliest opportunity"
They are also calling for the Dáil be reconvened next week.
Sinn Féin leader Gerry Adams has also said Mr Kenny should immediately resign and call a general election.
The party's deputy leader Mary Lou McDonald says if the Taoiseach is happy with his actions, he should have no problem accounting for them:
Meanwhile the Justice Minister Frances Fitzgerald has described the motion of no confidence from Fianna Fáil as a "sign of desperation".
The findings of the Fennelly Commission interim report say although she was not under any duty to do so, it would have been 'reasonable and prudent' Attorney-General for Maire Whelan to have contacted the Justice Minister about the taping of phonecalls in garda stations in March 2014, but she did not.
"What the Fennelly Commission finds is that the Taoiseach did not intend to put pressure on the Garda Commissioner - and it is important to note as well that when many ministers and others were making comments about the Commissioner, that the Taoiseach...expressed confidence when he was asked by the media about his role" she told the Pat Kenny Show here on Newstalk.
"All I can go on is the Fennelly Commission report, that's what the public can go on - what has actually been publsihed".
But Ms Fitzgerald says she is satisfied with Maire Whelan's actions. And she has also hit out at the motion of no confidence
Speaking to Newstalk Breakfast earler, Fianna Fáil leader Mícheal Martin said Mr Kenny’s behaviour in relation to the resignation of Martin Callinan is “neither credible nor tenable or acceptable”, and it “demands a motion of no confidence”.
In an attack on the Taoiseach’s handling of the Callinan affair, both at the time and in the 18 months since then, Mr Martin variously described the Taoiseach’s behaviour as: “absolutely disgraceful”, “shabby”, “contemptible”, “shifty” and “underhanded”.
The Taoiseach responded to criticisms by Mr Martin this morning, saying: “For Mícheal Martin to use words like that – I prefer to read the conclusions and accept the findings of the Fennelly Commission, conducted by a former eminent Supreme Court Judge, and the conclusions speak for themselves.”
Mr Kenny has been backed by Leo Varadkar, with the Health Minister offering unwavering support when speaking to Newstalk earlier this morning.
Mr Martin also hit out at the Labour party in the fallout from the Fennelly Commission report, saying it is "extraordinary" that the junior coalition party is continuing to support Kenny's position on his handling of the matter.
The Labour party’s position is “very, very weak” according to Mr Martin, following revelations that the Taoiseach did not consult with then Tánaiste and Labour Party leader Eamon Gilmore regarding his concerns, until Mr Callinan had made his decision to retire.
“I think it leaves Labour in a very, very weak position. I think it’s extraordinary that Labour continue to support the position of the Taoiseach in relation to this matter,” he said.
The Cabinet is due to meet at 10.30 this morning, for their first meeting since the summer break.
Listen below the full interview with Micheal Martin