Fianna Fáil and Sinn Féin plan to table motions of no confidence in Taoiseach Enda Kenny following the publication of the interim report of the Fennelly Commission yesterday.
Fianna Fáil has described the report as a "damning indictment of the actions of Enda Kenny".
Sinn Féin president Gerry Adams said the Taoiseach should resign immediately and call a general election.
The party "intends to introduce a motion of no confidence in the Taoiseach and the Government at the earliest opportunity and is demanding that the Dáil be reconvened next week".
The report concluded that a visit by the former secretary general of the Department of Justice Brian Purcell to the home of former garda commissioner Martin Callinan was the immediate catalyst for his retirement.
The report also found that the Taoiseach did not intend to put pressure on the commissioner to retire.
In a statement, Fianna Fáil's justice spokesperson Niall Collins criticised Mr Kenny's response to the report.
He said: "The Taoiseach’s actions regarding the departure of former commissioner Martin Callinan have unfortunately taken us to a position where we no longer have confidence in him and we will move a Dáil vote accordingly.
"The Dáil needs to debate in full all of the events detailed in the Fennelly Report.
"One issue that stands out very clearly is the level of panic and haste that surrounded the Taoiseach’s actions leading to Martin Callinan’s resignation.
"[That] a secretary-general of the Department of Justice was dispatched close to midnight to the commissioner’s home to tell him the Taoiseach may not have confidence in him the following morning beggars belief," Mr Collins said.
Gerry Adams said: "No amount of spin by the government or clever use of words in the Fennelly Report can disguise the fact that the Callinan debacle has revealed how dysfunctional this Government is.
"It is clear that the Taoiseach's deliberate actions led to the resignation of the garda commissioner. In effect, commissioner Callinan was sacked.
"The shameful defence of Enda Kenny by the Labour Party and by Fine Gael ministers is evidence of [how] far the government parties are prepared to go to protect their own narrow party political self-interest.
"The Taoiseach's position is untenable. He should resign. The Government's position is equally untenable. There should be a general election."
Sinn Féin deputy leader Mary Lou McDonald said the report raises questions about Enda Kenny’s credibility and any confidence that might remain in him as Taoiseach.
She added her party thinks the Oireachtas needs to be recalled.
Speaking on RTÉ’s Six One News, Deputy McDonald said Justice Fennelly was puzzled and perplexed by the Attorney General, Máire Whelan’s evidence and it is Sinn Féin’s view that her position is untenable.
Kenny unambiguously in the clear - Fitzgerald
Earlier, Minister for Justice Frances Fitzgerald said the report shows that the Taoiseach is unambiguously in the clear in the sequence of events that led to the retirement in March 2014 of Mr Callinan.
Speaking on RTÉ's Today with Sean O'Rourke, Minister Fitzgerald said it is a finding of fact that Mr Kenny did not intend to put pressure on the commissioner to retire.
The minister said the Cabinet is the only body that could have removed the commissioner.
She added that the purpose of the meeting with Mr Purcell at Mr Callinan's house, was to discuss the series of difficult issues that had arisen in the area of justice, prior to the Cabinet meeting on 25 August 2014.
Ms Fitzgerald said she has full confidence in Attorney General Máire Whelan and does not believe she "hyped" the issue of the recordings when she brought it to the attention of the Taoiseach.
She added that the actions of Ms Whelan were absolutely correct, in bringing the information to Mr Kenny as the issue was so serious and because that is who the Attorney General reports to.
She said following the meeting that night (24 August 2014), the decision of Mr Callinan to retire was his decision but he could have decided otherwise.
She said it is plausible to think that the commissioner could have come back with a response to Government as to how he was dealing with the issue of phone recordings.
Martin says Kenny 'shifty' over Callinan issue
Fianna Fáil leader Micheál Martin said the interim report is a damning indictment of the Taoiseach's approach to the entire issue and he comes across in the evidence, in his view as "shifty and underhand".
Speaking on RTÉ’s Morning Ireland, Mr Martin said that, essentially, Mr Kenny sent a messenger and emissary out to the home of Mr Callinan, an unprecedented event in itself.
He said Mr Callinan was told that the Taoiseach viewed the revelations concerning tape recordings in garda stations as a very grave matter and that in the event of it coming up at Cabinet the next day [and that it would be coming up], he might not be in a position to express confidence in the commissioner.
Mr Martin said: "Now in the real world that is effectively sacking the garda commissioner. He was left with no option, and the garda commissioner if you read the report is very, very clear...'I was left with no option' - he said".
Minister for Health Leo Varadkar said accusations from the Opposition that the Taoiseach moved to dismiss the former garda commissioner are incorrect.
Mr Varadkar said the report, which is available for everyone to read, debunks such charges.
He said the reason Mr Purcell was sent to Mr Callinan's home so late on 24 March 2014 was because of a Cabinet meeting the following morning.
He said the Taoiseach and the Attorney General were going to advise ministers at that Cabinet meeting of the potentially unlawful telephone recordings happening at some garda stations.
Mr Varadkar said Mr Kenny wanted Mr Callinan to know how serious he considered the issue to be and that because of its gravity "he may be in difficulty in expressing full confidence in him" if he was to be asked about it in the Dáil the next day.
The minister said it was expected that the commissioner would come back with some form of a response and that he would not resign.
He said the report shows that the Taoiseach did not set out to sack the former commissioner..
"What we have here are different accounts from different people. And you take any issue or event that involves five, six, seven people, you will get a slightly different account as to what they had to say.
"Judge Fennelly, a retired Supreme Court judge with very strong powers, was the only person who talked to all these people, and he came to his conclusion.
"So the central charge that has been made against the Taoiseach by the opposition and others that he somehow sought to sack the garda commissioner, that has been debunked by the findings of this Commission."
Analysis: Political Correspondent Martina Fitzgerald
To put it bluntly, the Government has the numbers and Enda Kenny has the support of the Labour Party so he will win the motion of no confidence in the Taoiseach.
Sometimes a motion of "no confidence" can suddenly turn into a "motion of confidence" with backbenchers rallying behind the Taoiseach.
It is an opportunity for the Opposition make the Taoiseach uncomfortable; try to embarrass him and to quote extensively from the Fennelly Report. That report says it was reasonable for Martin Callinan to believe that he was being asked to consider his position.
Minister for Justice Frances Fitzgerald has been out today staunchly backing the Taoiseach, saying the report was unambiguous and that he did not put pressure on Mr Callinan to retire or resign.
However, Fianna Fáil leader Micheál Martin is still maintaining the former garda commissioner was effectively fired.
Burton says reports clears Taoiseach of wrongdoing
Tánaiste and Labour Party leader Joan Burton has said the interim report has cleared the Taoiseach of any wrongdoing.
In a statement, the Tánaiste said the report made clear that the ultimate decision to step down lay with the former commissioner.
The Taoiseach said he prefers to "read the conclusions and accept the findings" of the report and declined to comment further as he arrived at Government Buildings this morning.
Meanwhile, Lecturer in Law at Dublin City University Vicky Conway said the evidence outlined in the interim report shows severe dysfunctionality in terms of the accountability mechanism between the garda commissioner and former Justice Minister Alan Shatter.
She said the commissioner is ultimately legislatively accountable to the minister directly and has a statutory duty to keep him or her informed of events. She said that between October 2013 and March 2014 when so much was going on, the evidence shows that there was not a single meeting between Mr Shatter and Mr Callinan.