"We believe she's booked further travel in New Zealand in the upcoming days".
She has not returned to her Auckland hostel in several days.
Millane's family sparked the investigation into her disappearance yesterday after they became alarmed when she didn't respond to birthday messages on Sunday.
Police confirmed a missing person's report was filed today for Millane.
The CCTV image, taken at Auckland's Sky City entertainment complex, was taken at 7.15pm on Saturday and is the last known sighting of her. "Please share and contact if you have any information regarding her whereabouts".
Her brother Michael said: "It was what she wanted - she wanted to see the world".
Mr Beard said various sightings have her wearing either a black top, blue jeans and red sneakers, or a black dress with white shoes.
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. She is approximately 5ft 6in (168cm) in height and 58kg. He said they were waiting for the British banks to update them on when Grace Millane's credit cards were last used.
Classic Aston Martins with Factory EV Powertrains Are a Thing Now
Aston Martin will use the same battery electric technology that will soon appear in their first all-electric model, the Rapide E. This is then mounted on the car's original engine and gearbox mountings, with power cords to feed the car's electrical systems.
Kate Middleton reveals Prince Louis is learning to wave
But I can't imagine how it feel when your loved ones are away on active service during Christmas. Thank you for your commitments and thank you for your sacrifices.
Santiago Solari praises out of favour Isco after Copa del Rey double
Scroll down for predictions , betting tips and odds, TV channel, head to head history and live stream information. It seems to me that at that age it's more handsome because he can truly value it. "I'm very happy with Isco".
She was just sight-seeing and travelling around New Zealand.
"Being out of contact with family for this long is especially out of character for her".
"At the moment, we don't have any evidence of foul play, but we keep an open mind", Detective Inspector Beard said.
"Last time we spoke to her she was in good spirits and was enjoying herself".
Grace Millane had been in New Zealand for about two weeks.
A spokesman for the Foreign Office said it is providing consular support to the family in the UK.
Base Backpackers declined to comment.
Beard said police have more than 20 staff working on the case and have been reviewing hours of surveillance camera footage from around the city, which has proved crucial in tracking Millane's movements.