A judge has addressed the grieving family of slain British backpacker Grace Millane, saying "your grief must be desperate".

Judge Evangelos Thomas was speaking this morning during the first court appearance of the man accused of the 22-year-old woman's murder.

The 26-year-old appeared in Auckland District Court after the discovery of Millane's body yesterday in the Waitakere Ranges

He walked into the dock at the Auckland District Court today wearing a blue boiler suit.

The Millane family was in court for this appearance.

"All of us hope that justice for Grace is fair and swift and ultimately brings you some peace," Judge Evangelos Thomas said at the outset of the hearing.

"That will not be happening today. There will be no judgment today."

He said there would be a number of procedural issues which would need to dealt with.

More than a dozen members of the press were also in court for the hearing, including several journalists from British television news stations and newspapers.

The public gallery was filled with dozens of people for the short appearance.

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

He sought interim name suppression for his client based on fair trial rights, which was opposed by police, the Millane family and press.

Judge Thomas declined the application for name suppression, however, Brookie instantly appealed the decision which automatically imposes a 20 working day suppression under New Zealand law.

Brookie added he has had "very limited disclosure" of evidence from police.

The barrister also opposed the several applications from the world's media to film the accused.

Judge Thomas 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 day.

"This is your first appearance, there are a number of media here wishing to cover the hearing."

The judge said the opening principle is for open justice and granted the media applications.

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

Judge Thomas also said the man, who did not apply for bail, is going to be a "high-risk remand prisoner".

Judge Thomas remanded him in custody without plea to the High Court on January 23.

Millane, an Essex woman 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 Saturday, December 1 entering CityLife Hotel with the 26-year-old accused of her murder.

Police have not confirmed how the pair met, and refused to comment on speculation they met on a dating app.

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

Flowers have been placed at the scene this morning.

Police said Millane's body was found about 4pm as a result of "investigative work".

Detective Inspector Scott Beard yesterday released two photos of a 2016 red Toyota Corolla hatchback linked to Millane's death.

The car was hired from a central Auckland rental company just before lunchtime last Sunday and was later found in Taupo.

Beard said the investigation team wanted to hear from anyone who saw the vehicle in the West Auckland area between 6am and 9.30am last Monday, December 3.

Beard, visibly emotional after delivering the news to Millane's family and then the media that a body had been found, said the focus of the investigation was now to piece together exactly what happened to the young woman.

"It is an unbearable time for the Millane family and our hearts go out to them," he said.