Patrick Sullivan, 25, a former French foreign Legionnaire and member of the republican splinter group, the Irish People's Liberation Organisation, was knifed to death in February 1992.
A west Belfast man was later convicted of his manslaughter.
His sister and brother met the police in Belfast on Friday morning.
Mr Sullivan was killed after confronting someone he suspected of anti-social behaviour in the Divis area.
He was stabbed in the neck and back and died from his injuries.
The family have always believed more than one attacker was involved and claim a post mortem examination that they have recently obtained backs up their assertion.
Patrick's sister, Margaret, and his brother, Seamus, accompanied by their solicitor, Padraig Ómuirigh , met detectives for an hour-long meeting on Friday.
The family would not reveal what had been said, but their solicitor said they hoped the new information they had would be enough to re-open the case.
"We had a constructive meeting with the police and hope to bring further information to them," said Mr Ómuirigh.
"The family have also lodged a complaint with the Police Ombudsman in relation to the standards of the original investigation and we also have a meeting with the ombudsman in the coming weeks."
When asked for a comment on the meeting, a police spokesman said: "We can confirm that local police met with members of the Sullivan family today."
The Police Ombudsman said: "We have received a complaint about the police investigation into the killing of Patrick Sullivan in Belfast in 1992.
"We are currently investigating the complaint, and investigators are due to meet Mr Sullivan's family on 30 August."
The family of a west Belfast man who was killed 20 years ago have called for a fresh investigation into his death.