As the first anniversary of the deaths approached, Mr Richard said the police were "very confident" but just needed "little bits" of information to solve the murders at Clydach last June.
Ioan Richard, of Craigcefnparc, said even those with an "anti-police attitude" should put their feelings aside to assist the investigation into the killings of Mandy Power, her two daughters and her elderly mother.
As the first anniversary of the deaths approached, Mr Richard said the
police were "very confident" but just needed "little bits" of information to solve the murders at Clydach last June.
The councillor added: "If the police knew the answers the jigsaw would be complete."
The bodies of Doris Power, 80, her daughter, Amanda, 34, and Amanda's two daughters Katy, 10, and Emily, eight, were all found at their semi-detached home in Clydach, near Swansea.
They had been beaten to death.
At the time, a team of 60 detectives were involved in the hunt for the killer.
Police have interviewed over 2,000 people in connection with the case and it has been featured on BBC's Crimewatch programme.
Woman suspect
Police had said there was no sign of forced entry at the family's home, which had been set ablaze by the killer.
Forensic scientists conducted a fingertip search around the family's semi-detached home.
South Wales Police later issued an e-fit picture of a woman suspect but she has not yet been found.
Police have interviewed over 2,000 people in connection with the case and it has been featured on BBC's Crimewatch programme.