"Sadly the evidence we have gathered to this point of the inquiry has established that this is a homicide", Detective Inspector Scott Beard told reporters earlier on Saturday.
More than two dozen police officers have been investigating the 22-year-old's disappearance since she was reported missing earlier this week.
"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. Beard said she met a man for a couple of hours on Saturday evening before surveillance cameras showed them entering the CityLife hotel at about 9:40 p.m.
Searches have also been carried out at the backpackers' accommodation where she was staying.
Grace last made contact with her family last Saturday, December 1.
"Somebody may find it somewhere, we don't know what has happened to it".
After visiting Peru, she arrived in New Zealand on November 20 and had been in near-daily contact with her family until 1 December.
Police continue to offer support to the Millane family, both in New Zealand and in the UK.
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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.
Detective Inspector Scott Beard said a scene examination at the hotel is continuing and investigators were progressing with the viewing of hundreds of hours of CCTV footage.
"I'm not going to speculate on how they met", he said.
They urged members of the public to come forward with any information.
On Saturday police released images of a pink watch and a necklace belonging to her and asked for the public's help in finding them.
Det Insp Beard confirmed today that the man being questioned by police on Saturday was the same individual.
This was her first time travelling overseas alone.
"Everyone who is a parent out there will understand and appreciate what the family is going through".
Described as "fun loving, outgoing and [a] family-orientated person", Millane was never out of contact with family and friends for this long, her family said.