Conor Murphy has again refused to state publicly that murdered south Armagh man Paul Quinn was not a criminal.
Northern Ireland's finance minister has been under pressure to make the public statement after retracting a claim he made 13 years ago that Mr Quinn had been involved in criminality.
Mr Quinn's mother Breege has repeatedly called for the Sinn Fein MLA to say publicly that her son was not a criminal, saying the slur on his name has compounded her family's grief.
The 21-year-old from Cullyhanna was beaten to death by a gang of around a dozen men in a farm shed across the border near Castleblayney, Co Monaghan, in 2007.
His family blame members of the IRA, but Sinn Fein has long denied republican involvement.
The killing became one of the talking points of the Irish election as Mr Quinn's mother called for the former Newry and Armagh MP to be removed from his post as a minister over the comments.
Sinn Fein faced criticism from political rivals over its response to the killing.
Mr Murphy was urged by Ulster Unionist MLA Robbie Butler and TUV leader Jim Allister during a Stormont Assembly sitting on February 10 to make a public apology to the Quinn family.
He responded then: "I made a statement last week and I have written to that family."
On Monday, as he appeared at his first press conference at Stormont since the row, Mr Murphy refused to publicly state Mr Quinn was not a criminal.
"I made a statement in relation to that, I have written to the family and my offer to meet the family remains, I am happy to meet them at any time," he said.
Mrs Quinn has said she will not meet Mr Murphy until he publicly states her son was not a criminal.
When pressed by the PA news agency, Mr Murphy added: "I made a statement, I am content to meet the family at any time and discuss these matters with them."
