The 22-year-old from Essex hasn't been seen since she entered downtown Auckland's CityLife Hotel in the company of a 26-year-old man last Saturday evening.
Today, Detective Inspector Scott Beard said that man — named as a person of interest yesterday — has been taken to Auckland Central police station and was speaking to investigators "in relation to the murder of Grace Millane".
"Sadly the evidence we have gathered to this point of the inquiry has established that this is a homicide."
Police still didn't know where Millane was — but were determined to return her to the family who have spread word of the talented artist and university graduate's disappearance worldwide since her daily social media contact with family stopped the night before her 22nd birthday on Sunday.
Millane's father David, a millionaire property developer, flew into New Zealand early yesterday.
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.
Police had spoken to Millane's family this afternoon, Beard said.
"They're devastated."
Officers found the 26-year-old man at a central Auckland address at 3pm, and interviews were still taking place late this afternoon.
A vehicle of interest had been secured and police were trying to find out exactly where the vehicle had been since Millane's disappearance. He wouldn't give a description of the vehicle or say where it was found.
This morning police released photos of a necklace and pink Casio Baby-G watch Millane was thought to be wearing when she disappeared, and said her passport was also missing.
They still wanted to hear from anyone who had seen any of the items, or the black dress and white sneakers Millane was wearing when she was last seen.
"You know, that property is going to be somewhere. Her clothing's going to be somewhere, we haven't found it, and somebody may find it."
CCTV footage captured Millane leaving Andy's Burgers & Bar, on the first level of Sky City, at 7.15pm last Saturday, December 1.
At 9.41pm Millane and the 26-year-old man taken in by police today were seen on CCTV entering CityLife Hotel, which has entrances on both Queen and Durham streets.
Police had found identified the man by yesterday and spoken with him before he was taken to Auckland Central police station today.
Asked why police were now treating Millane's disappearance as a murder, Beard said it was a combination of factors.
"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."
Police had "no reason or understanding what the motive was", he said.
Millane and the man being interviewed by police were together on Saturday evening and went to a number of places before going into CityLife Hotel.
When asked if Millane knew the man before the evening she disappeared, Beard would only say that "we don't have any evidence of that at this stage", and wouldn't comment on whether the pair met on Tinder.
"All I can say is that we know they were together from the time at the Sky City Hotel ... I'm not going to speculate on how they met. This issue here is Grace is still missing and we want to find her."
Beard wouldn't say whether police had seen footage of the man leaving CityLife Hotel or if he thought Millane was killed in the hotel, a large apartment-style complex.
Police yesterday identified an apartment of interest and a scene examination by police and forensic experts was still taking place, he said.
They had received "a lot" of phone calls from the public and those were being "worked through and prioritised".
"But as you can appreciate the focus is on the 26-year-old male and also finding Grace."
An emotional Beard said it had been a tough time for all involved in the investigation.
"Everybody who is a parent will understand what the family is going through ... our hearts go out to them."
That was especially so for David Millane, as police had met the distraught father, but also for other family in the United Kingdom, including Millane's mother Gillian, unable to travel to New Zealand because she was recovering from an operation.
"I know that the thoughts of all New Zealanders will be with Grace's family tonight and I want to reassure both everyone here and abroad that New Zealand police are determined to do everything we can to find her."
• Anyone with information on the disappearance of Grace Millane can contact police on 0800 676 255.
