"I want to reassure the public police are determined to do everything we can to find her".
Detective Inspector Scott Beard said police had gathered evidence on Saturday that had "established this is a homicide".
He said: 'Just after 3pm this afternoon (Saturday) a 26-year-old man was located at a central Auckland address by police.
"I know that the thoughts of all New Zealanders will be with Grace's family tonight", Beard said.
Police investigating the murder of British tourist Grace Millane stand by a cordoned off crime scene along a section of Scenic Drive in the Waitakere
"We now have a last known sighting of Grace at 9.41pm at the Citylife Hotel, on Saturday, December 1, with a male companion".
Several of her belongings, including her passport, are missing and police believe it is likely Grace had these items with her, Auckland Police Detective Inspector Scott Beard said today.
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 last Sunday.
Her passport is also missing.
He wouldn't speculate where Grace was killed, Beard said.
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"We don't know what's happened to the property of hers that has been missing", he said.
"I want to reassure everyone, both here and overseas, that New Zealand Police are determined to do everything we can to find her".
Her father David Millane fronted a press conference at Auckland Central Police Station on Friday after flying to New Zealand from Essex.
Police had spoken to Millane's family this afternoon, Beard said.
Police have been conducting a scene examination at a unit in the hotel.
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China has said it will immediately implement measures agreed under a trade war "truce" with the US. It was unclear if Gao was referring to the tariffs in his remarks to reporters.