The Dáil has voted confidence in Ceann Comhairle Verona Murphy following a lengthy debate.
The motion was passed by 96 votes to 71, with two abstentions.
The debate came after angry scenes in the chamber last week when a Government proposal to allocate new speaking time to the Regional Independent Group and coalition backbenchers was passed.
It was the first time in the history of the Dáil that such a vote took place in a ceann comhairle.
Following the result, Ms Murphy said she wanted "to assure all members on all sides" that she beared "no ill will and my door is always open".
"I will continue to uphold my solemn declaration to vindicate the rights of all members and administer the rules chosen by members of this house impartially and fairly," she added.
Earlier, the Sinn Féin leader accused Ms Murphy of an "unprecedented and, frankly, breathtaking" failure to perform the duties of her office.
Mary Lou McDonald claimed that she had "actively and enthusiastically" taken "a wrecking ball" to Dáil procedures.
"This marks a fundamental departure from established practice, making a mockery of the oath taken by the Ceann Comhairle."
Ms McDonald warned that the Dáil could become "a token platform" and detailed what she said were three failures by Ms Murphy to perform her duty, all of which were done to "cheers of approval" from Government benches.
The Sinn Féin leader said Ms Murphy's position was untenable, even if she survived the motion.
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Dáil prone to pyrotechnics even after speaking rights row
The Labour Party leader said the office of Ceann Comhairle had been dragged into a mess of the Government's own making.
"Her position has become untenable because of a deal between the Government and Michael Lowry and his group," Ivana Bacik told the Dáil.
She said the big question was why the Government was going to such lengths to facilitate Mr Lowry and nobody knew what was in the "secret grubby deal".
Members of Mr Lowry's own group would not even sit beside him, Ms Bacik added, but Fianna Fáil and Fine Gael members would stop at nothing to defend his deal.
Social Democrats deputy leader Cian O'Callaghan said the Government leaders were part of the re-establishment of Mr Lowry, putting the Independent TD at the heart of the coalition and bending over backwards to make him happy.
Mr O'Callaghan said the office of Ceann Comhairle should not have been gifted as part of the deal with independents as the move undermined years of Dáil reform and opened up the office to charges of bias.
Backbench deputies were instructed to vote for an agreed candidate for chair, he said.
"So Fianna Fáil and Fine Gael cut a deal with a convicted tax cheat and corrupt politician," Mr O'Callaghan said.
Solidarity-People Before Profit TD Paul Murphy accused the "right-wing Government, without a mudguard" of "creeping authoritarianism" and preparing to "ram through" a series of "highly unpopular measures".
"We won, you lost, we can do whatever we want," is how he characterised the coalition's handling of the speaking rights row.
His colleague, Richard Boyd Barrett, said the Government does not care about corruption and will do anything to stay in power.
Opposition behaved in 'juvenile and despicable' manner, says Lowry
The Opposition have behaved in a "juvenile and despicable" manner, according to Independent TD Michael Lowry.
In a statement after a confidence motion in the Ceann Comhairle passed, Mr Lowry said that proceedings in the Dáil "marked a significant victory for democracy".
"The past three months have been crippled with venom and spite from the opposition parties," he said.
"Their actions have been both juvenile and despicable. It has been a very difficult time for the regional independent group, simply because we had the courage to step up to form a strong and stable Government."
He said the Opposition "took a trouncing" and that their actions were condemned "for what they are - orchestrated obstruction".
"Ultimately, all they succeeded in doing is strengthening the position of the Ceann Comhairle," added Mr Lowry.
"With 96 votes in her favour, Verona Murphy's credibility is not only secured, it has been endorsed."
He said the Regional Group of Independents has secured its "justified" speaking rights.
"We are fully recognised," he said.
"Government must now be permitted to get on with their work in the face of the unprecedented challenges that lie ahead for Ireland and Europe."
Dáil hears of 'strategy of aggression and destruction'
The Taoiseach denounced the Opposition bid to oust the Ceann Comhairle as a "strategy of aggression and destruction".
Micheál Martin said it was profoundly regrettable that the discussion was held as there was nothing in Ms Murphy's behaviour to justify the attempt to remove her.
He said the Opposition had mounted a campaign of aggression and disruption that was wildly disproportionate and had at its core the demand that the minority should have the right to import mob politics into the chamber.
"The arsonists are demanding that we censure the fire brigade," he said.
Tánaiste Simon Harris said that it was incumbent on TDs to get on with their work.
He told the Dáil that they stand on the precipice of extraordinary economic turbulence globally and people who got up this morning, who have gone to work and are genuinely worried about the uncertainly of the economy.
Mr Harris said the parliament has a duty to show leadership at a time of crisis and a potential global trade war which will have consequences for Ireland.
"The time for shouting, hooping and hollering is over," he added.
The Ceann Comhairle was accused by five Opposition groups of failing to apply the Dáil rules during the lead up to last week's vote.
Sinn Féin, Labour, Social Democrats, Independent Ireland and Solidarity-People Before Profit alleged that Ms Murphy colluded with the Government parties to get the proposal over the line.
