Auckland Police Detective Inspector Scott Beard said a 26-year-old man is being questioned in relation to Grace Millane's whereabouts.
This afternoon police said they had assessed Millane's property left at the backpackers where she was staying - and found some items missing.
In the statement issued on Saturday, Millane's family praised Auckland police "who have been outstanding in their support and efforts in helping to find Grace". "We are determined to find her and return her to her family".
Grace Millane, 22, from Essex in the United Kingdom, was last seen in central Auckland on December 1 and was reported missing on Wednesday.
The Lucie Blackman Trust, which has been supporting Millane's family, posted on its Facebook page that they were "incredibly saddened" by the police announcement.
"The family are devastated, everybody who is a parent out there will understand what this family is going through".
'Several of her belongings, including her passport, are missing and police believe it is likely Grace has these items with her'.
Grace's father today said: "Grace is a lovely, outgoing, fun-loving, family-orientated daughter".
"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, 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.
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Within a week, she was in a coma, and her family made a decision to take her off life support. Doctor Charles Cobbs said his patient, a woman in her 60s, filtered her neti pot water.
DI Beard confirmed that the man being questioned by police on Saturday was the same individual.
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.
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.
"She arrived here on the 20th of November, and has been bombarding us with numerous photographs and messages of her adventures", Millane said.
Police want the public to help find this necklace belonging to backpacker Grace Millane.
David Millane, the father of missing backpacker Grace Millane, says his daughter has "never been out of contact for this amount of time".
"Our hearts go out to them".
Searches have also been carried out at the backpackers' accommodation where she was staying.
He said police were working on reviewing hours of surveillance camera footage from around the city, which has proved crucial in tracking Millane's movements.
He wouldn't speculate where Grace was killed, Beard said.
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