The Garda Commissioner has said disciplinary proceedings have been initiated against a number of gardaí following the penalty points report carried out by an Assistant Garda Commissioner.
Martin Callinan said he could not comment on the Minister for Transport Leo Varadkar's statement.
The statement said that he believes that the Garda Síochána Ombudsman Commission should now investigate the penalty points controversy.
However, Commissioner Callinan pointed out that the report has already been referred to the Garda Inspectorate and the Oireachtas Justice Committee.
Minister for Transport Leo Varadkar earlier said he believes the Ombudsman Commission should now investigate the penalty points controversy.
Mr Varadkar said that his department and the Road Safety Authority have studied the report by gardaí into the termination of penalty points.
Speaking on RTÉ's Morning Ireland, the minister said he agrees with the RSA that a further investigation is needed.
He said he had no doubt that gardaí had taken the investigation seriously and had taken steps to "tighten up the system".
However, Mr Vardakar said he believed that there were questions still to be answered.
He said: "Reading through the report, particularly reading the appendices and the different cases, I have to say that I got the sense, not so much that they'd looked at the underbelly of this, but that in a lot of cases they were explaining away penalty point terminations that to the reasonable person seemed a little bit unusual.
"The RSA is now proposing that there be a further investigation by the Garda Ombudsman Commission. I think that's a good suggestion."
Mr Varadkar said it was important that the public had confidence in the penalty points system, and believed that if discretion was being employed, it was being employed equally.
The minister said he would be introducing legislation later in the year to tighten the penalty points system, including introducing a graduated licence system for learner drivers.