Grace Millane's family say they are staying positive and hope she returns home soon.
The 26-year-old man was questioned by detectives after he was traced by police to at an address in central Auckland on Saturday afternoon. (AAP) The last confirmed sighting of Millane was at 9.41pm the same day at the Citylife Hotel in central Auckland, when she was seen with a "male companion".
Detectives said yesterday they were continuing to view hundreds of hours of CCTV footage, while they continue to examine the CityLife Hotel in central Auckland, where she was last seen entering with a man on Saturday night.
News of the murder inquiry comes hours after Millane's family said they were "staying very positive" as the search for her continued.
"We still do not know where Grace is", Detective Inspector Beard said.
Investigators had said yesterday that they held "grave fears" for Grace's safety.
"We know that he was with her on the Saturday evening and went to a number of places before going to the Citylife Hotel", he told reporters.
Millane had been in New Zealand for two weeks, the UK's Press Association news agency reported.
"He was brought back to the Auckland Central Police Station and is now speaking to us in relation to the murder of Grace Millane".
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Tonight's statement said the Millane family have requested privacy at this time and will not be making any further statements at this stage.
"The evidence we have located so far, our scene examination, from the CCTV footage we have and our investigation has determined that Grace is no longer alive and this is a murder investigation". "This issue here is Grace is still missing and we want to find her".
He wouldn't speculate on how they met.
Police released images of Ms Millane's watch and necklace earlier on Saturday.
Grace's father today said: "Grace is a lovely, outgoing, fun-loving, family-orientated daughter".
In a tearful press conference on Friday, Ms Millane's millionaire father, who has travelled to Auckland, said the "fun-loving" graduate's family are "extremely concerned" for her welfare.
'She arrived here on the 20th of November and has been bombarding us with numerous photographs and messages of her adventures, ' Mr Millane said.
He tearfully explained that his daughter has never been out of contact with her family for such a long period of time, usually contacting them on social media.
Anyone with information that could help with the investigation has been asked to contact 0800 676 255.
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After a missing person report was filed, New Zealand police released an image of Ms Millane at a late night casino in Auckland. He said they had been in contact with the British High Commission in Wellington.
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