(CNN) The family of murdered Grace Millane has thanked the country's people for their compassion and said the British backpacker "will forever be a Kiwi."

Millane's father David flew out to New Zealand and has visited the site where her body was found. He and Grace's uncle, Martin, also took part in a traditional Maori blessing of the site.

"Grace was not born here and only managed to stay a few weeks, but you have taken her to your hearts and in some small way she will forever be a Kiwi," the family said in a statement released on Wednesday.

Her family said Millane set out to travel the world in mid-October, arriving in New Zealand on November 20. "By the amount of pictures and messages we received she clearly loved this country, its people and the lifestyle," they said in a statement released on Wednesday.

They thanked Auckland Police for carrying "out the most concise, stringent and thorough investigation" into the "heinous crime."

"We all hope that what has happened to Grace will not deter even one person from venturing out into the world and discovering their own overseas experience," the family added.

They thanked New Zealanders for their "outpouring of love, numerous messages, tributes and compassion."

Body returned to family

The 22-year-old was last seen in central Auckland on December 1. Police ended their search on Sunday after finding her body in a wooded area in the Waitakere Ranges, west of the city.

Her body was formally identified and returned to her family in New Zealand, Auckland City Police said on Wednesday.

"They [her family] are in the process of organizing to take her home, in the next few days," Detective Inspector Scott Beard said.

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

Police are looking for a shovel believed to be related to the inquiry. They said in a statement on Tuesday that they don't know where the item is and that they would like to hear from anyone who may have found it after December 3.

Suspect not identified

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

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

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 in custody until he appears in court in January, the broadcaster reported. Thomas addressed Millane's family members at the court hearing, RNZ said.

Police at the scene where a body was found.

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

Detective Inspector 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.

Prime Minister apologizes

The country's Prime Minister Jacinda Ardern apologized to Millane's family on Monday. She said Millane should have been safe on her trip to New Zealand, a place that prides itself on manaakitanga -- a word from the Maori, New Zealand's indigenous Polynesian people -- meaning hospitality.

"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."