Garda Commissioner Nóirín O'Sullivan has said the revelations over penalty points and garda breath test discrepancies are "totally unacceptable and not in keeping with the standards of a modern and professional police service".
In a statement, the commissioner said that as An Garda Síochána is on a journey of radical reform "it is inevitable that we will identify more examples of bad practice".
It has emerged more than 14,500 people who were prosecuted for road traffic offences are to have their convictions quashed because of garda error.
It was also revealed that from 2011 to 2016, the number of drink-driving tests gardaí claimed to have carried out was hugely exaggerated, by over 937,000.
Earlier, Taoiseach Enda Kenny said the revelations over discrepancies were "not acceptable".
Speaking in Rome, Mr Kenny said: "I would like the [Garda] Commissioner to be very clear in her statement that she makes...It's not acceptable.
"I've already expressed confidence in the Garda Commissioner a number of times. I would like to see her statement this afternoon. I continue to have confidence in her."
Commissioner O'Sullivan said she has written to the Policing Authority seeking further review by the Garda Inspectorate of the discrepancies between real and claimed breath tests.
She said it is a problem that goes back more than a decade and new processes for gathering and collating statistics have been in place since April 2016.
The commissioner said: "This is an issue – as the Authority has pointed out – which is more than systemic. It’s about ethics. It’s about supervision. It’s about measurement. Most of all, it’s about trust".
She said she has asked the Policing Authority to consider requesting the Garda Inspectorate to:
Examine the processes and methodology utilised to identify the nature and extent of the problems.
Review the control measures put in place designed to address the issues.
Examine if the current processes regarding roadside breath testing are in line with best practice.
Her statement added that the Policing Authority and Garda management are of the same mind that the discrepancies identified in the systems are a "matter of individual and collective ethical behaviour and not one of occasional systems failure".
Fianna Fáil's justice spokesperson Jim O'Callaghan has described the statement as inadequate.
He said explanations are needed about how this happened, not more reviews.
Mr Kenny is in Rome to celebrate the 60th Anniversary of the signing of the Treaty of Rome and told reporters during the event that "it's not for government to interfere in the running of the gardaí, it's an internal matter.
"The minister [for Justice] has set out her strong view on this, and has expressed that very strong view to the Garda Commissioner.
"Clearly the government have made changes here, to the strengthening of GSOC, the strengthening of the Garda Inspectorate, and the setting in place of the independent Garda Authority, which I believe will change the culture of the gardaí over the next number of years."
Tánaiste Frances Fitzgerald said the scale of the latest garda scandal is "appalling and staggering".
Minister for Social Protection Leo Varadkar echoed the view of his party colleagues, saying the revelations are appalling but he does have confidence in the Garda Commissioner.
Mr Varadkar said if it is a question of "is she part of the problem or part of the solution", he would say she is part of the solution.
He also said he does not expected all 14,700 convictions to be overturned, but expects it to be close to a third of the convictions.
Meanwhile, Green Party leader Eamon Ryan said Commissioner O'Sullivan should consider her position and described the exaggeration of drink driving tests as "fake policing".
He said serious questions must be asked about whether the team that is currently leading the force is capable of cleaning up the system.
When asked if the Commissioner's position was tenable, Mr Ryan said "I don't think it is", adding, "she should consider her position based on what happened this week".