David Millane arrived in New Zealand on Friday morning, after the family raised the alert earlier in the week, having not heard from Grace since Saturday (December 1) - which he said was unusual.
Police say Grace Millane was last spotted entering CityLife hotel in Auckland's CBD with a man on Saturday.
The 22-year-old, from Essex, vanished in New Zealand a week ago. "We don't have any evidence of foul play but we're keeping an open mind", Mr Beard said.
"Her family are devastated", he said.
"We still don't know where Grace is", Beard said, who added police have identified a vehicle of interest today.
Miss Millane's body has not been found, but Det Insp Beard said police were "determined to do everything we can to find her".
"The man is the same one who was named as a person of interest yesterday".
The revelation follows a forensic examination of a hotel where she was last seen on Saturday 1 December with a "male companion".
Grace Millane's watch is a pale pink Casio Baby-G.
Police said enquiries into Grace's disappearance have not led to further confirmed sightings of her.
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Fighting back tears, he told a press conference: "Grace is a lovely, outgoing, fun-loving, family-orientated daughter".
Police would like to hear from anyone who may have seen any of the items matching their descriptions over the past week.
Detectives have since assessed Grace's belongings, which were left at the backpackers where she was staying.
He wouldn't speculate where Grace was killed, Beard said.
New Zealand Police continue to examine hundreds of hours of CCTV footage.
He said Ms Millane had a number of phones on her while in New Zealand. Grace has never been out of contact for this amount of time and is usually in daily contact with either her mother, myself or her two brothers.
"Grace started this travel journey in Peru in South America and was really looking forward to the second leg in New Zealand".
"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".
Anyone with information about the missing items has been advised to contact 0800 676 255.