David Tamihere, who has lost his appeal for the murder of the two Swedish backpackers Sven Höglin and Heidi Paakkonen is being called on "to do the right thing".
Police say the Court of Appeal judgement upholding his conviction is right and just.
Court of Appeal judges concluded that Tamihere is still guilty beyond reasonable doubt for the 1989 murders.
Assistant Commissioner Paul Basham, told Morning Report the only shadow lingering over the case was that Paakkonen's body has never been found.
Police vindicated over David Tamihere appeal failure
Officers who worked on the case, including all those who searched for Paakkonen's body, were among those who would like to be able to return it to her family.
"We would dearly like to do that. We think it's the right thing to do and we call upon Mr Tamihere to do the right thing," he said.
A police informant's claim - that Tamihere killed Höglin with a piece of wood and dumped the bodies at sea - was exposed as false in 1991, when Höglin's skeletal remains were found near Whangamatā, more than 70km from where the Crown said the murders occurred.
The Court of Appeal judges found while false evidence from a jailhouse informant at the original trial did constitute a miscarriage of justice, they remain satisfied "beyond reasonable doubt" that Tamihere murdered the young couple on the basis of other evidence.
Regarding the reliance on the inmate's evidence, Basham said police would take any lessons that needed to be learned on board for their future investigations.
"Police are rightly sensitive to the decisions of our courts ... and so we where we are getting clear directions from the court we take every effort to adopt those directions and incorporate them into our everyday approach to investigation and the way we police in New Zealand."
These days police took a cautious approach to the use of inmate informants' evidence, Basham said.
There were a lot of safeguards in the system in the way evidence was introduced and / or challenged.
"So I think overall on balance these things are resolved successfully through the courts where there is an issue on a particular form of evidence."
The court's decision validated the long-standing police case against Tamihere.
"We feel the case against Tamihere has always been strong and the decision from the Court of Appeal this week in our view reinforces that position."