(CNN) British backpacker Grace Millane should have been safe on her trip to New Zealand, a place that prides itself on manaakitanga, the country's prime minister said

Jacinda Ardern invoked manaakitanga -- a word from the Maori, New Zealand's indigenous Polynesian people, meaning hospitality -- in delivering an apology to the 22-year-old's family. She was speaking during her weekly post-Cabinet news conference, Radio New Zealand reported.

"From the Kiwis I have spoken to, there is this overwhelming sense of shame that this has happened in our country, a place that prides itself on its hospitality, on its manaakitanga, especially to those who are visiting our shores," Ardern said.

"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."

A 26-year-old man accused of killing Millane made his first appearance in a New Zealand's Auckland District Court Monday, RNZ reported.

Millane was last seen at the Auckland city center December 1. A body believed to be that of the missing woman was found in a wooded area in the Waitakere Ranges, west of central Auckland, police said Sunday.

Police previously said that a man seen with her in Auckland the night she disappeared would be charged in her death.

Suspect not identified yet

Presiding Judge Evangelos Thomas denied the man's request to have his name suppressed, but his defense lawyer immediately appealed that decision, meaning he cannot be publicly identified for 20 days, RNZ reported.

The man -- who appeared in court wearing a blue jumpsuit -- was remanded to custody until he appears in court in January, the broadcaster reported. Thomas addressed Millane's family members at the court hearing, RNZ said.

"I don't know what we say to you at this time. Your grief must be desperate," it quoted him as saying. "All of us hope that justice for Grace is fair, swift and ultimately brings you some peace."

Tributes to Grace Millane were placed at the start of the road near where her body was found in West Auckland.

Detective Inspector Scott Beard said Sunday afternoon that the body found in the Waitakere Ranges was yet to be identified.

"The formal identification process will now take place. However, based on the evidence we have gathered over the past few days, we expect that this is Grace. Obviously this brings the search for Grace to an end," Beard said in a statement. "It is an unbearable time for the Millane family, and our hearts go out to them."

Beard issued an appeal for sightings of a 2016 red Toyota Corolla hatchback hired from a rental company.

"The focus now is to piece together exactly what happened to a young girl, who came to this country on her (worldwide trip)," he said.

Family privacy

An autopsy of the body has been completed, but the results will not be released, Beard said.

He said that the investigation is continuing and that police have received several reports of sightings of the red hatchback.

Beard discouraged people from sharing the accused man's name while it is being withheld in court.

Police at the scene where a body was found.

"We would like to remind the public that whilst we appreciate the public feeling around this case, it is an offense to breach a court order such as a name suppression, and this includes naming someone who has name suppression on social media," Beard said.

The Millane family has asked for continued privacy, Beard said.

"We have been approached by a number of people who would like to hold vigils for Grace. The Millane family are very grateful for the kind thoughts and give their blessing to these vigils, but have respectfully declined to attend," he said.

'Fun-loving, family-orientated'

Millane's father, David Millane, issued a statement through police Friday appealing for information and describing his daughter as "a lovely, outgoing, fun-loving, family-orientated daughter."

Grace Millane's father, David Millane, addresses media.

He said his daughter was on a yearlong worldwide trip.

"Grace started this travel journey in Peru in South America and was really looking forward to the second leg in New Zealand. She arrived here on the 20th of November and has bombarded us with numerous photographs and messages of her adventures," he said. "We are all extremely upset, and it is very difficult at this time to fully describe the range of emotions we are all going through."

Murder case

Local police who had been searching for Millane for days announced on Saturday that new evidence had changed the course from a missing person investigation to a murder case.

"The evidence we have located so far -- our scene examination, CCTV footage and our investigation -- has determined that Grace is no longer alive and this is a murder investigation," Beard said Saturday.

Police had earlier said that the last known sighting of Millane was of her entering a hotel at about 9:40 p.m. on December 1 and that they were conducting an examination of an apartment at the hotel.