The Ceann Comhairle has said she intends to continue in her role in the face of a motion of no confidence by the opposition.
Verona Murphy also “categorically” rejected accusations of partisanship made by the opposition.
A motion of no confidence in Ms Murphy was drafted by the opposition after they called into question her handling of a protest in the Dáil on Tuesday.
Ms Murphy declared that the rules of the Dail had been amended by the Government as opposition TDs stood and repeatedly raised their objections.
Leaders of the main opposition parties met on Wednesday morning to discuss their response.
Sinn Féin leader Mary Lou McDonald later told Ms Murphy that her actions were “demonstrably partisan” and lacked the “impartiality and independence demanded of your position”.
She said her position was untenable and asked her to reflect on this.
A drafted motion of no confidence was published on Wednesday evening and is to be submitted by opposition parties Sinn Fein, Labour, the Social Democrats, Solidarity-People Before Profit, and Independent Ireland.
The motion seeks to note “that the Ceann Comhairle no longer retains the confidence of all members of Dáil Eireann”.
In a statement, Ms Murphy responded to say she had “loyally, scrupulously and impartially” carried out the role as Ceann Comhairle and rejected “false accusations of partiality and collusion”.
“Prolonged disorder and obstruction is utterly unacceptable in any democratic parliament,” she said.
“So too is making false accusations of partiality and collusion against its officials and chair.
“By virtue of the independence of the office of Ceann Comhairle, I am in the unenviable position that I cannot descend at will into debate to defend myself against the entirely false allegations of collusion made against me in the Dail today.
“I categorically reject these unfounded allegations. I have at all times followed the correct procedures of the House and the advice of the impartial officials present.
“I fully intend to continue to carry out the onerous office to which I was elected, in accordance with the solemn undertakings I gave the Dail upon my election.”
The clerk of the Dáil, Peter Finnegan, in a report about Tuesday’s proceedings, said that after Ms Murphy put the Order of Business to the Dáil on Tuesday, TDs who said “Votail” to trigger a division were not audible.
He concluded that all decisions taken by Ms Murphy, given the “great disorder”, were in compliance with the rules of the Dail and her powers as Ceann Comhairle.
“The Ceann Comhairle cannot allow a situation where disorderly conduct is allowed to frustrate the business of the Dáil. Otherwise, the Dail would be unable to discharge its constitutional functions,” he said.
“Ultimately, the Constitution provides that all decisions are made by a majority of the members present and voting.”
Minister for Culture and Media Patrick O’Donovan said Ms Murphy’s position was still tenable, despite losing the confidence of the opposition.
“She will have the support of the majority of the Dail, we live in a democracy,” Mr O’Donovan told RTÉ Radio.
“None of these people voted for her in the first instance, so I’m not surprised that they wouldn’t have confidence in her.
“I’m not surprised that they will be looking for the first opportunity to remove her. Who are you codding?”
Earlier on Wednesday, Ms McDonald and other opposition leaders questioned the Ceann Comhairle’s role after Tuesday’s proceedings.
“So, who convinced you to play your part in this disgraceful charade, or is it simply that bias for the Government is baked into the very deal that secured your position?” Ms McDonald asked the speaker.
“That is now the question.”
The Sinn Fein leader continued: “Ceann Comhairle, not alone have you lost the confidence of the entire opposition; you have, in fact, decimated it.
“The Dail cannot function properly whilst you remain in the chair.
“Above all, the Ceann Comhairle must be impartial, fair and independent, and by your actions you have demonstrated that you are not.
“Your position is therefore untenable.
“So, I ask you to reflect very carefully on this, because you need to go.”
Labour party leader Ivana Bacik said she did not believe Dail rules had been applied “fairly and impartially” by Ms Murphy.
“That is why this morning, together with my parliamentary part,y we agreed to ask to reflect on your position over the coming days,” she said.
“If not, if necessary, we will have no option but to table a motion of no confidence in you. And I regret that it has come to this.”
There were chaotic scenes of shouting, interruptions and allegations of misogyny on Tuesday as weeks of tension over the speaking rights row boiled over during Leaders’ Questions.
Ms Murphy faced continual interruptions as she tried to continue proceedings as opposition TDs took to their feet and objected to the Government’s proposals to change speaking time arrangements.
She declared the changes to the standing orders passed before adjourning the Dail. However, opposition leaders insist the vote was not properly conducted.
They also accused her of earlier pushing through the Government’s proposed order of business for the Dail without acknowledging an opposition request for a vote.
The row has its origins in the formation of Ireland’s current coalition involving Fianna Fail and Fine Gael, supported by several independent TDs.
Some of those independents have been appointed as junior ministers while the others had sought to join an opposition technical group for the purposes of speaking time, despite supporting the formation of Government.
The controversial changes to standing orders include the creation of new speaking slots for coalition backbenchers and Government-aligned independents, a reduction of time for contributions on debating the order of business, and a halving of slots for Taoiseach’s Questions.
Opposition parties are vehemently opposed to the changes, characterising them as an attempt to dilute their ability to hold the Government to account and to blur the relationship between the independents who have supported the formation of the coalition.
The dispute delayed Micheál Martin’s nomination as Taoiseach in January and has trundled on despite several inter-party meetings and the intervention of the Ceann Comhairle, in favour of the opposition.
Tensions boiled over on Tuesday with the Dail witnessing angry scenes as Ms Murphy presided over a vote on the changes.
Mr Martin has accused the opposition of trying to bully and intimidate Ms Murphy, and said it “marked a new low” for the opposition.
Responding in the Dáil on Wednesday, Mr Martin accused Sinn Féin of pursuing a “destructive model of opposition” and trying to bring the “loudhailer politics of the street” into the Dáil.
He told Ms McDonald: “Your stated objective here is to undermine this institution, to undermine the Government, to reduce the Government majority and to create mayhem. That is what you are about.”
Fianna Fáil leader Mr Martin said the opposition’s “intimidatory barracking” of newly-elected TDs marked a “new low” for behaviour in the Dáil.
He expressed concern that the Dail “would never be the same again” after the scenes witnessed on Tuesday.
Social Democrats deputy leader Cian O’Callaghan said it was essential that the Ceann Comhairle enjoys the confidence of both government and opposition.
“Clearly, this is no longer the case. I do think you need to reflect on that position,” he told the Dáil.
