New Zealand Prime Minister Jacinda Ardern reacts at a press conference when she spoke about murdered British tourist Grace Millane. Picture: Mark Mitchell/New Zealand Heralds via AP

Wellington, New Zealand - New Zealand Prime Minister Jacinda Ardern choked back tears on Monday while offering a heartfelt apology to the family of murdered British backpacker Grace Millane, as the man accused of killing the young traveller made his first court appearance.

Her voice cracking with emotion, Ardern said there was a collective feeling of shame in the South Pacific nation over the fate of Millane, whose body was found Sunday in parkland just outside Auckland.

"There is this overwhelming sense of hurt and shame that this has happened in our country, a place that prides itself on our hospitality, on our manaakitanga," she said, using the Maori word for welcoming others.

"So on behalf of New Zealand, I want to apologise to Grace's family - your daughter should have been safe here and she wasn't, and I'm sorry for that."

Ardern told reporters at her weekly media conference that New Zealanders were heartbroken for Millane's family and were feeling her death personally.

Millane disappeared on December 1, on the eve of her 22nd birthday, and her family's worst fears were confirmed when her body was found on Sunday.

The death has shocked New Zealand, which is usually regarded as a safe place to travel and averages less than 50 homicides a year in a population of 4.8 million.

A 26-year-old man, who cannot be named for legal reasons, faced Auckland District Court on Monday charged with her murder.

Wearing a blue prison-issue boiler suit, he was not required to enter a plea and was remanded in custody until January 23.   

Millane was on a year-long worldwide holiday after graduating from university and had been in New Zealand for two weeks after travelling around South America for more than a month.

It was her first solo overseas trip and her family became alarmed when she failed to maintain her habit of staying in daily contact.

Police had previously said she was last seen alive entering an inner-city hotel in Auckland with a man.

CCTV image released by New Zealand Police shows 22-year-old English tourist Grace Millane in central Auckland. The image was captured on Saturday night, about 7:15 p.m. and is the last known sighting of Millane, whose 22nd birthday was the next day. Picture: NZ Police via AP

Her father David flew to New Zealand after she went missing and issued an emotional appeal for information relating to his "fun-loving, outgoing and family-orientated" daughter.

Judge Evangelos Thomas opened Monday's brief court proceedings by addressing the family, Radio New Zealand reported. 

"I do not know what to say to you, your grief must be desperate," he said.

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