The authority said there is an unacceptable level of service to victims
The Policing Authority say they have "serious concern" of performance failures in the O'Higgins Report, which were identified by previous inquiries.
Following a meeting with Garda Commissioner Noirin O'Sullivan, the authority say they will hold two meetings in public next month for more detailed discussion on the issues.
The agendas for these meetings are likely to focus on service to victims, protected disclosure and culture - and may also examine the O'Higgins recommendations in the context of other reviews, such as those of the Garda Síochána Inspectorate.
The Policing Autority said there was "deep unease" at the organisation and management culture, including the environment for speaking out as evident in the report.
It also said there is a need for "an urgent response" by An Garda Síochána to the findings and recommendations in the O'Higgins Report.
The body is also concerned that "good work being done by gardaí every day can be set to nought" while doubts remain about these issues.
These issues include service to victims, culture, training and formation, issues of governance, management and supervision.
"The unacceptable level of service to victims, which had such devastating consequences for them, poor individual performance, poor supervision and related management responsibility were raised with the Garda Commissioner", the Policing Authority says.
"In relation to the treatment of victims, the Commissioner described the reforms which have been implemented over the past 12 months - including the victim liaison offices and the improved incident management system".
"Mindful of the impact on rank and file gardaí, the authority welcomed that particular attention has been paid to the current staff in Bailieboro by garda management".
The Policing Authority also expects to see a formal garda response to the findings and recommendations made by Judge O’Higgins.
The Commissioner was also questioned on the steps which senior gardaí take on an ongoing basis to encourage and facilitate 'speaking up' about wrongdoing in the force.
Speaking after the meeting, Policing Authority chairperson Josephine Feehily said: "The recurring deficiencies in policing performance evidenced in the O’Higgins final report are deeply troubling".
"We wish to express our particular concern for the impact on the victims of crime who were entitled to expect a professional and competent service from the Garda Síochána and who didn’t get it".
"We welcome the Garda Commissioner’s apology to victims, her immediate acceptance of the Commission findings and her acknowledgement that there are many lessons to be learned".
"However in exercising its oversight role, the Authority will seek evidence of a tangible response to those lessons including at the two forthcoming public meetings in June".
"Today was just a first step in this oversight process and there is clearly a lot of work to be done", she added.