The family of murdered prison officer Brian Stack say they have received an apology from the Garda Commissioner for the failures of Garda investigations into the crime.
The family met Commissioner Drew Harris for an hour-and-a-half this morning.
They say the commissioner was unable to give them any explanations for the failures and have now called on the Minister for Justice to appoint an independent police expert to examine the issues.
They also say they were told a file will be sent to the Director of Public Prosecutions but they believe it is unlikely that there will be any prosecutions.
The Chief Officer at Portlaoise Prison died in hospital in September 1984, 18 months after the shooting, but no-one has been charged or convicted in connection with the murder.
In a statement, Commissioner Harris said he offered the family "an apology for the failings and shortcomings in the investigation. I fully acknowledge that these matters are serious and had a detrimental impact on the investigation".
He said the murder investigation remains open and appealed to anyone with information to come forward.
The Stack family claim key witnesses were not interviewed, material evidence such as fingerprint records and exhibits have gone missing and critical intelligence was not acted upon.
The family said this relates to the identities of the gunman, a motorcyclist and the person alleged to have sanctioned the murder.
The most recent investigation by the National Bureau of Criminal Investigation, which commenced in 2009, was only completed this year and its report is with Commissioner Harris.
Brian Stack's son, Austin, described the meeting with the Commissioner as "full and frank".
He said the family will ask the Minister for Justice to consider allowing an independent policing expert from outside the State to carry out a full review into the investigation, which he said, Commissioner Harris is open to.
Speaking on RTÉ's Today with Sean O'Rourke, Austin Stack said: "He did give us a verbal apology ... It's important, particularly to my mother, because it's an acknowledgement from An Garda Síochána, and de facto the State, that there were errors. That a lot of mishandling went on, that the investigation was not as it should have been.
"I think that the next step would be for the Taoiseach to do something similar."