Solidarity-PBP TD Brid Smith has called on newly appointed Garda Commissioner Drew Harris to meet the families of the Miami showband victims for an anniversary ceremony in Dublin on 31 July.
Three members of the popular band were taken from their tour bus and shot dead on a country road after a gig in Banbridge, Co Down in July 1975.
Deputy Smith also called on the Government to delay the appointment of Mr Harris until he meets the families and addresses their concerns.
In the Dáil, she said the families had been waiting 43 years for justice and had been denied files in this State.
With Mr Harris' appointment, she said there would be a situation "where the head of the PSNI, then garda commissioner, has access to files about their loved ones that they can't get access to".
However, Minister for Justice Charlie Flanagan said the Government would not be delaying the appointment of Mr Harris, which he described as "particularly significant".
He said the incoming commissioner is a person of "huge ability and the highest integrity".
"I know he has enormous respect for and knowledge of An Garda Síochána, having worked with members of the organisation as close colleagues over the course of his career," Mr Flanagan said.
The minister also said that dealing with the legacy of the troubles on this island is a complex and sensitive task, and one to which there are no easy solutions.
He said the appointment of Mr Harris would serve to cement good working relationships between the PSNI and the Garda Siochána.
Ms Smith also accused Mr Harris of blocking files being released to the families of victims of the so-called Glenanne Gang, who attacked Catholics in the 1970s.
