Det Insp Scott Beard said the evidence told them she was "no longer alive".
Grace Millane's family has asked for privacy.
A priest from backpacker Grace Millane's hometown in the United Kingdom has called the news of her death "devastating".
"We still do no know where Grace is".
He added: "Today were have identified and secured a vehicle of interest, and we are now making enquiries to find out exactly where that vehicle has been". He would not confirm what type of vehicle it was.
Beard said they "still do not know where Grace is" but they were "determined to find her and return her to her family".
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The trust was "incredibly saddened" by the news.
New Zealand police confirmed they are now treating British backpacker Grace Millane's (pictured) disappearance as a homicide.
She last made contact with her family last Saturday, December 1, and was formally reported missing on Wednesday, December 5.
"Grace's watch is a pale pink Casio Baby-G and her necklace is described as silver and round with a green stone in the middle of it".
According to the newspaper, the police arrived at this conclusion after studying "evidence uncovered during the investigation, including CCTV footage and scene examinations".
Police had been interviewing the unnamed 26-year-old about Millane's disappearance, and said Saturday that they would charge him with her murder.
A British backpacker missing in New Zealand since last weekend was murdered, police said.
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Police have not yet found the body of the 22-year-old from Wickford in Essex.
A tearful David Millane appealed to the public to come forward with any information, "no matter how small".
She arrived in New Zealand last month and was last seen on the night of December 1 entering a central Auckland hotel with a 26-year-old man.
Millane was last seen at a hotel with a man, who has not been named.
"Several of her belongings, including her passport are missing and police believe it is likely Grace has these items with her".
Miss Millane, who graduated from the University of Lincoln in September, had been travelling alone in New Zealand for two weeks, following a six-week group trip through South America.
Her birthday was on Sunday, but she didn't contact her family.
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