Grace Millane should have been safe here.

Instead she was killed - her body dumped in bush just metres from a rural road.

The man accused of the British backpacker's murder was labelled a "scumbag" by a member of the public as his first court appearance ended yesterday.

It's a case which has tugged on the heart-strings of the nation and has provoked emotion from those used to dealing with such horrific crimes.

At the outset of the hearing the judge addressed the Millane family, acknowledging how difficult it must be for them.

"Your grief must be desperate," Judge Evangelos Thomas said.

"All of us hope that justice for Grace is fair and swift and ultimately brings you some peace."

Dressed in a blue boiler suit and only turning his head on occasion towards his lawyer, the 26-year-old defendant was under the glare of dozens of members of the international media and public as he stood in the dock at the Auckland District Court for about an hour.

"A lot has happened in the last two days," the man's lawyer, Ian Brookie, said.

Millane's body was found just 10m off Scenic Drive in West Auckland's Waitakere Ranges on Sunday - a week after her 22nd birthday.

A post mortem examination was conducted yesterday but the results would not be released by police.

However, court documents viewed by the Herald indicate police believe Millane was killed between December 1 and 2.

The man accused of killing her will keep his identity hidden until at least early next year.

An application for interim name suppression was declined by Judge Thomas and opposed by the Millane family, police and the collective press.

Brookie, however, instantly indicated he would appeal Judge Thomas' decision not to grant name suppression for his client, which automatically imposed a 20 working day suppression order under New Zealand law.

The barrister also opposed several applications from international media to film the accused.

But Judge Thomas granted the media's applications, and told the defendant: "As you will know the allegations that you face and the background to them have been the source of much media coverage over the last eight or nine days.

"If you do go to trial it will be some time away, a lot of water will have passed under the bridge."

The accused, who did not apply for bail, was remanded in custody without plea until his next appearance in the High Court on January 23.

The court appearance came just a day after the top cop in charge of the investigation, Detective Inspector Scott Beard, was visibly emotional as he addressed the media and revealed her body had been found.

Prime Minister Jacinda Ardern also choked up as she spoke of the case yesterday afternoon.

Millane, who recently graduated from university, came to New Zealand as part of a year-long solo OE.

She arrived in Auckland just days before she was killed. Millane was last seen on CCTV on December 1 entering CityLife Hotel with the murder accused.

Last night police said the Millane family did not wish to comment further but were aware of several vigils organised around the country.

"The Millane family are very grateful for the kind thoughts and give their blessing to these vigils, but have respectfully declined to attend," a police spokesperson said.

The police's investigation, code-named Operation Gourami, remains in its infancy and officers have more work ahead. A scene examination at Scenic Drive will continue today, and there are renewed calls from police for anyone who saw a 2016 red Toyota Corolla hatchback.

The car was rented and returned to a central Auckland rental car company last Monday at lunchtime.

Police said last night the vehicle was located in Taupo but not driven there by her alleged killer.

"It was then hired by persons unrelated to the investigation, who travelled to Taupo in the vehicle. Police then identified the car as a vehicle of interest on Saturday December 8, at which time it was located and seized," a police spokesman said.