The family of the only prison officer to be assassinated in the Republic believe they know the identity of his killer after new evidence came to light in recent weeks.
The father-of-three was shot in the back of the neck on March 25, 1983, on a busy Dublin street after leaving a boxing contest at the National Stadium. Paralysed and brain-damaged from the shooting, he suffered for a further 18 months before dying from his injuries at the age of 47.
Austin Stack, who followed in his father's footsteps and is now assistant governor of Dublin's Wheatfield Prison, said he will be asking Mr Adams to use his influence to help secure an IRA admission and apology.
"I am confident I know the identity of the killer and the identity of the individual who sanctioned it, and I want Gerry Adams to talk to his organisation and try to get people who know something to talk to us," he said.
Mr Stack has been gathering evidence from a number of sources on his father's murder over recent years.
But he said corroborating evidence received in the last month has convinced him of the identities of the gunman, his getaway motorcycle driver and the man who sanctioned the killing within the IRA leadership.
His family have now ruled out any possibility of organised crime gang involvement in the shooting. They are certain their father was assassinated because of the strict security regime he implemented at Portlaoise, which housed all republican prisoners at the time.
He added: "I don't know whether Gerry Adams can tell us who carried out the murder. Gerry Adams had connectivity with an organisation that carried out a lot of murders and I don't know if he will bring to the family any information that isn't presently either available to the family or An Garda Siochana. But I do know that the appalling murder of Brian Stack has been re-investigated by An Garda Siochana."