Beard said police questioned the man seen with her that night and have named him as a person of interest - but he has not been taken into custody.
Police would like to hear from anyone who may have seen any of the items matching their descriptions over the past week.
Detective Inspector Scott Beard told media on Thursday the lack of contact was out of character for Ms Millane, especially as it was her birthday last Sunday.
Beard said the investigation had progressed rapidly since identifying the last sighting of Millane at CityLife hotel in central Auckland at 9.41pm last Saturday, and the police had received a huge amount of information from the public.
Police have released photographs of a necklace and a watch missing from the belongings Grace Millane left at the hostel where she was staying. "At this point, we hold grave fears for her safety". "We don't have any evidence of foul play but we're keeping an open mind", Mr Beard said.More news: SpaceX rocket booster misses landing as supplies sent to space
"We don't know what's happened to the property of hers that has been missing", he said.
"Grace's family have been advised of this development and are devastated".
Her father David Millane fronted a press conference at Auckland Central Police Station on Friday after flying to New Zealand from his home town of Essex in the United Kingdom.
Grace Millane's belongings, including a necklace and a Baby-G watch.
Police were continuing to view "hundreds" of hours of CCTV footage, and the scene examination of the CityLife hotel was still underway, police said on Saturday afternoon.More news: Stranger Things 3: The Game Is Creeping Onto All Platforms
"We have a couple of phones from the backpackers but we believe she may have another one or two so we're keeping an open mind", he said.
"Many of these calls have been from members of the public, offering accommodation and assistance to the Millane family".
Police continue to offer support to the Millane family, both in New Zealand and in the UK.
Millane graduated from the University of Lincoln in September before beginning her trip.
"We thought maybe it's just the time zone, sort of catching up, but we looked into it and realised her messages hadn't been read or delivered". "She's usually in daily contact with family on social media", he said.More news: Marvel Ultimate Alliance 3 revealed, and it's only on Switch
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