The Garda Commissioner has said that an agreement gardaí had with those in charge of the funeral of Alan Ryan was not abided by.
Martin Callinan said he was disappointed by this and that gardaí heard three shots being fired over the 32-year-old's coffin last Saturday morning.
The Commissioner said the senior officer in charge made a decision in the public interest not to intervene during the paramilitary display at the funeral.
Mr Callinan said that he stood over that decision as Commissioner.
He said it was a highly-charged atmosphere and that the safety of the public was the primary consideration of gardaí on the day.
Mr Callinan described what happened at the funeral as appalling and said gardaí intend to bring those responsible for firing the shots to justice.
Earlier, Minister for Justice Alan Shatter defended the gardaí who did not intervene after a volley of shots was fired at the funeral.
Mr Shatter said those on duty had to make "proper and mature" judgments, adding that there were people at the funeral who would have been happy to bring about "a major confrontation".
He said that innocent lives could have been lost if gardaí had intervened.
The minister repeated his description of some of the events at the funeral in Dublin at the weekend as scandalous and unacceptable.
Speaking on RTÉ Radio this morning, Minister Shatter said what happened "took us back to the dark days of the troubles".
He said an investigation is now under way and he has full confidence in the Garda Commissioner to take appropriate action.