A man appeared in court yesterday charged with the murder of Mr Skudder, who had been missing for three years.
While the skeletal remains have yet to be formally identified, police believe they are Mr Skudder's.
"I know there are people out there who know the circumstances of Harold's disappearance, and I ask those people to come forward and contact the police," Detective Inspector Shane Cotter said yesterday.
The discovery of the remains followed a tipoff to police and followed the arrest on Thursday and court appearance yesterday of a 26-year-old man who has been charged over the historic murder.
The man was granted interim name suppression to inform his family of the charges he faced. Police opposed suppression.
The man was remanded in custody until March 25.
Mr Skudder's mother reported the 38-year-old missing in January 2008, a year after his disappearance.
"They (Mr Skudder's family) are pleased that there's been a resolution in the matter, but they're obviously very upset that Harold has been killed," Mr Cotter told Radio New Zealand.
"Again, they're awaiting the identification of the skeletal remains so that if it is Harry, they're able to lay him to rest properly."
Mr Skudder had four children, and was living a transient lifestyle at the time he disappeared which was part of the reason he was not reported missing for 15 months.
Police said they were not looking for anyone else in relation to his disappearance, but are keen to speak to people who know about his disappearance.
Police yesterday searched a house in the Lower Hutt suburb of Stokes Valley. Mr Skudder had connections with the people who used to live next door, Mr Cotter said.