Officers in Auckland have been speaking to a 26-year-old man in connection to her disappearance and he will remain in custody until Monday morning, when he will appear in the Auckland District Court.
Police had spoken to Millane's family this afternoon, Beard said.
David Millane, father of missing British tourist Grace Millane, speaks to the media as police give updates on the investigation.
"Everybody who is a parent will understand what the family is going through. our hearts go out to them".
Det Insp Beard added: "We still do not know where Grace is".
"We still do not know where Grace is", Detective Inspector Beard said.
Grace Millane's family say they are staying positive and hope she returns home soon.
"I know that the thoughts of all new Zealanders will be with Grace's family tonight, and I want to reassure everyone both here and overseas that New Zealand Police are determined to do everything we can to find her", he said.
The 22-year-old, from Essex, vanished in New Zealand a week ago.
Police say Grace Millane was last spotted entering CityLife hotel in Auckland's CBD with a man on Saturday.
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A CCTV image shows she was at Sky City, a hotel a short distance away, at 7.15pm on the same night - but her whereabouts between those two sightings is unknown.
Police want the public to help find this necklace belonging to backpacker Grace Millane.
Police said enquiries into Grace's disappearance have not led to further confirmed sightings of her.
The announcement follows a review of CCTV footage, the forensic examination of a hotel where she was last seen on Saturday 1 December, and the discovery of a vehicle.
Fighting back tears, he spoke to media about the "lovely, outgoing, fun-loving, family-orientated daughter" who had been so looking forward to going to New Zealand and had "bombarded us with numerous photographs and messages of her adventures" since arriving.
News of the murder inquiry comes hours after Millane's family said they were "staying very positive" as the search for her continued.
The watch is a pale pink Casio Baby-G.
The necklace is described as silver and round with a green stone in the middle of it.
She has not been seen or heard from since.
Police said they had received dozens of calls to a hotline and more than 25 staff were working on the case, trawling through hours of CCTV footage to trace her movements.
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