New Zealand Prime Minister Jacinda Ardern on Monday made an emotional apology to the parents of murdered British backpacker Grace Millane.

"From the Kiwis I have spoken to there is this overwhelming sense of hurt and shame that this has happened in our country," she told media.

"So on behalf of New Zealand I want to apologize to Grace's family: Your daughter should have been safe here and she wasn't and I'm sorry for that," Ardern added.

Earlier in the day a 26-year-old man appeared in an Auckland court and was charged with the murder of the 22-year-old tourist.

The accused, who has been in police custody since Saturday, was granted interim name suppression. He was remanded in custody without entering a plea and is expected to appear at the High Court on January 23.

The presiding judge in Auckland acknowledged the presence of the slain woman's family.

"Your grief must be desperate," Judge Evangelos Thomas said according to Radio New Zealand.

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

Police on Monday said a post-mortem examination had been carried out, but results would not be released.

The circumstances of Millane’s death are still not clear. She was last seen entering a hotel in central Auckland with the accused on December 1, one day before her 22nd birthday.

Her family in Britain became concerned when Millane didn't respond to their birthday wishes.

Police on Sunday found her body while searching for her near a road at the Waitakere Ranges about 25 kilometres west of central Auckland.

Police were still looking for sightings of a car that was rented for a 24-hour period and returned to central Auckland rental car company on Monday 3 December at lunchtime, Detective Inspector Scott Beard said in a statement.

Beard said Sunday he did not know if Millane knew the man before and would not speculate how she had met him.

New Zealand was the second stop of a planned year-long worldwide overseas experience of the advertising graduate and artist, from Essex, which she started in South America.