The Justice Committee has called on the garda inquiry to prioritise the resignation of former garda commissioner Martin Callinan and the handling of information at the Department of Justice and report back on those two items within eight weeks.
It is also calling for the inquiry to be conducted in public, in so far as is practicable.
In a statement, the committee also reiterated that it reserves the right to conduct its own examination into these and related matters as it sees fit.
Meanwhile, Garda Superintendents Association President Pat McCabe has said the Commission of Investigation will get to the bottom of “legacy issues”.
Speaking at its annual conference in Kildare, Superintendent McCabe said the association was not aware that non-emergency calls were being recorded in garda stations
The superintendent also said the Garda Ombudsman Commission is referring too many cases to them for investigation and that GSOC should conduct its own inquiries
He said the association, which represents 120 superintendents, does not accept that An Garda Síochána is corrupt.
Supt McCabe says allegations of widespread corruption and malpractice in the force are simply not true.
However, the superintendent accepted mistakes have been made but said these are now being rectified
He also said that while whistleblowers may not get everything right, their concerns have to be listened to
He also welcomed the establishment of the Commission of Investigation, which he believes will get to the bottom of what he described as legacy issues.
The Association President said he could not comment on the resignation of the former garda commissioner Martin Callinan because he did not have all the facts.
However, he said Mr Callinan had been a dedicated policeman and on a human level it was very difficult for him and his family.
Minister for Justice Alan Shatter said he phoned the former Garda Commissioner following his resignation to wish him well, but he declined to comment on the circumstances of Mr Callinan's departure.
He was speaking at the Garda Superintendents Conference, which tonight refuted allegations of widespread corruption or malpractice within the force.
The Minister spoke about issues as diverse as confidentiality, racial profiling and failures of management and administration when he addressed the Garda Superintendents this evening but he was not prepared to talk about the circumstances surrounding the resignation of the former Garda Commissioner.
The Association of Garda Superintendents insisted today that most of them did not know that non-emergency calls were being recorded in garda stations and they rejected the assertion that the Garda Síochána is corrupt.
The association also said it agrees with the Oireachtas Justice Committee that the Commission of Investigation should report on the circumstances surrounding the resignation of the former Commissioner Martin Callinan within eight weeks.
The Minister declined to speak about the matter except to say that Martin Callinan was a very distinguished officer and he phoned him to wish him and his family well.