Police took the 26-year-old suspect into custody earlier this week and have charged him with Grace's murder.
Police are investigating the disappearance of 22-year-old British woman Grace Millane after last been seen on Saturday December 1 in Auckland. He is due to make his first court appearance on Monday.
A group of 18 staff, including forensic experts, search the bush area for most of Sunday.
On Sunday afternoon, police scoured a bush area along Scenic Dr in the Waitakere Ranges, where they found a body believed to be Millane's.
"All of us hope justice for Grace is fair and swift, and ultimately brings you some peace".
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Judge Thomas acknowledged the Millane family, who were present in court, and said he recognised the enormous grief they must be feeling.
Her father, David Millane, arrived in NZ on Friday, and made an emotional public appeal for help in finding Grace, who he described as a "lovely, outgoing, fun-loving, family-orientated daughter".
Her father, David Millane, said they last had contact on the day she vanished. "The focus now is to piece together exactly what happened to a young girl who came to New Zealand".
"I am releasing two photographs of a 2016 red Toyota Corolla hatchback", Beard said in a statement.
Grace Millane's body was found in the Waitakere Ranges yesterday.
She had not been seen since December, when she was last seen alive at a hotel with a man.
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Millane told journalists his much-loved daughter arrived in New Zealand on November 20 as part of a year-long, worldwide overseas experience that began earlier this year in South America.
The Lucie Blackman Trust, which has been supporting Millane's family, posted on its Facebook page they were "incredibly saddened" by the police announcement. She had been travelling the world after graduating from college.
Members of her family flew out to New Zealand from England the day before the police announced her death.
A man has been charged in connection with her murder.
Police have released two photographs of a 2016 red Toyota Corolla hatchback was hired from a central Auckland rental vehicle company just before lunchtime on Sunday.
"We were praying for her while she was missing, and then of course. the sad realisation that she wasn't missing any longer, as it were".
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Grace arrives in Auckland and checks into the Base Backpackers Hostel. It isn't clear if the same man is being held by police.