The man who killed police Constable Matthew Hunt is appealing his "crushing" sentence - one of the longest jail terms in New Zealand history.

But the Crown has pushed back, saying the "cold, unprovoked" killing caused "the highest level of concern to the public".

Convicted cop killer Eli Epiha was made to stand throughout the one and a half hour appeal hearing because of to a broken chair in the audio-visual link room at the prison.

In the Court of Appeal in Wellington, his lawyer Marcus Edgar said the sentencing judge erred when deciding not to factor in a certain piece of case law, and gave "insufficient recognition" to Epiha's personal circumstances.

Epiha was convicted of murder after gunning down two unarmed police officers after fleeing a traffic stop and crashing his car in West Auckland in 2020.

Hunt, 28, was killed by a shot in the back while his partner, Constable David Goldfinch, was badly wounded by four shots to the lower body.

Epiha admitted killing Hunt but denied it was intentional. He was, however, sentenced on the basis the murder was intentional. He was also sentenced for attempting to murder Goldfinch, and reckless driving causing injury to a bystander.

Constable Matt Hunt was murdered while on active duty. Photo / Supplied

Justice Geoffrey Venning sentenced him to life imprisonment with a 27-year non-parole period, making the sentences one of the longest in New Zealand.

In the appeal today, Edgar said the case of Daniel Luff was "set aside" by Justice Venning, but should have been used to help him come to a starting point for sentence.

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Daniel Luff was 17 when he was sentenced to life imprisonment with a non-parole period of 17 years in 2002 for shooting and killing a policeman in Manawatu.

Edgar said the matter was set aside for a number of reasons, including the age of the case and the different types of firearms used in the respective offences.

But he said Luff carried many similarities with Epiha's offending, including that it involved murdering a police officer, the attempted murder of another, and shooting at a third.

Diane Hunt, the mother of slain police officer Matthew Hunt, is supported by family friend and National MP Mark Mitchell outside the High Court at Auckland. File photo / Michael Craig

Choosing not to use Luff to help determine the sentencing "suggested Mr Epiha was 45 per cent more culpable for similar offending".

Edgar also said the judge didn't factor in or didn't give enough recognition to factors such as Epiha's guilty plea to the murder, his age, or any ability for rehabilitation.

"A crushing sentence imposed on what is still a young man failed to uphold an important principle of sentencing – that of rehabilitation."

Crown lawyer Brian Dickey said the way Epiha shot Hunt and Goldfinch showed it was a "determined effort to kill police officers".

What was "remarkable" in the case was the lack of a reason for the offending.

Eli Epiha at an earlier court appearance for the murder. Photo / Brett Phibbs

"Mr Epiha had no motive to kill these police constables. He was just killing them . . . and with respect, that's what led His Honour Justice Venning to speak of how chilling this was.

"It was such a cold, unprovoked killing of uniformed constables just doing their job.

"That just triggers the highest level of concern for the public in the future."

Epiha had no history with and didn't know the officers, who were getting out of the car to go to his aid after he crashed.

Dickey also said the late guilty plea for murder offered little relief to Hunt's family so it was correct for the judge to offer only a small discount for it.

The Court of Appeal will release its decision in writing at a later date.