Brian Stack, chief prison officer at the high-security Portlaoise Prison, was shot in the back of the neck as he left a boxing match in 1983.
He was left paralysed and died 18 months later.
The issue was raised by Fianna Fáil leader Micheál Martin.
Mr Martin did so after it emerged, during Ireland's general election campaign in February, that Mr Adams had emailed Irish police commissioner Noírín O'Sullivan a list of four republicans who may have been involved.
The Sinn Féin leader said he had been given the names by Austin Stack, himself a senior prison officer and son of Brian Stack.
But Mr Stack, who with Mr Adams met a senior republican with knowledge of his father's murder more than two years ago, denies handing over any names.
The secret meeting took place after a journey in a blacked-out van.
In the Dáil (Irish parliament), Taoiseach Enda Kenny accused Mr Adams of knowing more about the murder, which is still being investigated.
Mr Kenny said he is to due to meet Austin Stack soon.
Mr Martin accused Mr Adams of withholding information about a murder and of "living in a parallel universe where rules apply to everyone" except republicans.
The Sinn Féin leader, in a brief comment, said he did not know who the killers were and had "acted in good faith" for the Stack family.
He accused Fianna Fáil of attempting to exploit the controversy in "a cynical and contemptible way".
Sinn Féin leader Gerry Adams has offered to make a statement to the Irish parliament about his knowledge of the murder of a senior prison officer in the Republic of Ireland in 1983.