The Tánaiste, Mary Harney, has told the Dáil she will speak to the Minister for Justice about the possibility of him making a Dáil statement on Dean Lyons.
Mr Lyons was wrongfully arrested and charged in connection with the murder of two women in Grangegorman in Dublin in 1997.
The Labour leader, Pat Rabbitte, had asked for such a statement from Minister Michael McDowell, saying there remained a necessity for a more detailed explanation than the apology from the gardaí published today.
Mr Lyons, who died four years ago, was arrested shortly after the killings, but had made a false confession.
The Lyons family has welcomed the garda statement.
They say they understand why the gardaí arrested their son and they are not bitter about the fact that it took almost eight years for the force to acknowledge Dean's innocence and apologise.
They also say that it helps to bring closure to the matter and they will not be seeking any financial compensation for the trauma they have suffered.
However, speaking on RTÉ's Morning Ireland, Stella Nolan, the sister of one of the two murdered women, Sylvia Shiels, called for a public inquiry into the garda handling of the case.
