Fianna Fáil and Sinn Féin have said they have no confidence in Ceann Comhairle Sean Barrett.
It follows Mr Barrett’s defence of his decision to rule out a debate on the setting up of a Commission of Inquiry into allegations of garda malpractice.
Fianna Fáil TD Dara Calleary said the party does not have confidence in the Ceann Comhairle.
Speaking on Cormac ag a Cúig on RTÉ Raidió na Gaeltachta, Mr Calleary said: "At this moment, because of what the Ceann Comhairle said this morning, we do not have confidence in him.
"We would like him to withdraw what he said, and if he does that confidence will be restored. This is very serious."
He added Fianna Fáil had not discussed a no-confidence motion in the Ceann Comhairle at this point.
Meanwhile, Sinn Féin President Gerry Adams rejected a claim by the Ceann Comhairle that Sinn Féin is attempting to undermine him.
Mr Adams said: "What happened in the Dáil around the motion to establish a commission of investigation into claims of Garda malpractice was a farce.
Earlier, the Ceann Comhairle had said his decision to cancel a Dáil debate on the creation of a commission of inquiry into allegations of malpractice in a garda division was not influenced by any letter from former minister Alan Shatter.
Mr Barrett said that he took the decision for the motion proposing the commission to be put to the house without debate so the investigation could go ahead immediately.
The Dáil had been due to debate the terms of reference of a proposed commission to inquire into incidents in the Cavan-Monaghan garda division recommended in a report by barrister Sean Guerin.
Mr Shatter is challenging aspects of Mr Guerin's report and the Dáil debate on the matter was blocked after legal objections by the former minister.
Speaking on RTÉ's Today with Sean O'Rourke, he said the decision he took was not influenced by any letter from Mr Shatter.
He said: "I received a letter from a firm of solicitors addressed to the Ceann Comhairle of Dáil Éireann, not a personal letter from Alan Shatter.
"I took a decision in the interest of the public so that an investigation can proceed immediately without the possibility of the Houses of the Oireachtas being hauled to the High Court and this matter being delayed and thousands of euro being spent on legal fees."
Mr Barrett said Mr Shatter's issue was that he did not want his name included in the terms of reference.
The Opposition staged a walkout of the Dáil on Wednesday in protest at the decision, while there was further criticism from Fianna Fáil and Sinn Féin in the Dáil yesterday.
Fianna Fáil leader Michael Martin described it as "appalling" that a TD would go to such lengths to silence the Dáil.
Speaking the same programme, he said the Dáil was silenced on an issue of fundamental importance to the administration of justice.
"I think it is reprehensible that a Dáil deputy would initiate a process designed to prevent the Dáil from debating issues of fundamental process.
"That goes against the heart of parliamentary policy and Deputy Alan Shatter should not have done that," he said.
Mr Martin also said that he was disappointed with what Mr Barrett had said on the programme earlier in relation to the inquiry.
He said: "The terms of reference of a commission of investigation were not technical, that's misleading by the Ceann Comhairle to say that.
"They go to the very heart of the issues that were inquired into by Mr Guerin or the rationale for the establishment of the inquiry."
Sinn Fein's Padraig Mac Lochlainn said Mr Barrett's decision has set a dangerous precedent.
Speaking on RTÉ's News at One, Mr Mac Lochlainn said we are into very dangerous territory if a member of the Oireachtas, through their solicitor, can prevent a debate on matters of serious importance.
Mr Mac Lochlainn said it was preposterous for the former minister to argue that a High Court judge could be influenced by statements read out in the Dáil.
He said it was unacceptable that the Ceann Comhairle had facilitated that argument.
Minister for Jobs, Enterprise and Innovation Richard Bruton this morning said when the Ceann Comhairle makes a decision, political parties should accept it and move on.
Speaking at the regional publication of the Government's latest Action Plan for Jobs in Ballina, Co Mayo, Mr Bruton said he felt people were not interested in procedural wrangling between the Mr Martin and Mr Barrett.
Mr Bruton said the Ceann Comhairle was an independent manager of Dáil business and had a job to do.
Minister for Finance Michael Noonan has said he accepts Mr Barrett was acting on the best legal advice.
Independent TD Mick Wallace said that there is no logic in killing the debate on the setting up a commission of investigation.
He claimed that since last Summer, it is been almost impossible to get debating time on policing issues.
He told RTÉ's Drivetime that it is unfair to deny a debate on the issue and that he has been waiting for months to discuss it