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Detective Inspector Scott Beard said police were dealing with the UK family of Ms Millane, who went missing in New Zealand a day before her 22nd birthday.
Police yesterday released a photograph showing the last known sighting of Ms Millane. Taken from CCTV security footage, it shows the young woman dressed in a black dress and white shoes, with her brown hair down.
The image was captured on Saturday night, about 7.15pm, in downtown Auckland near SkyCity, police said. It is the last time anyone has seen Ms Millane.
Police were speaking to people at the backpackers where Ms Millane was staying - including those she was with on Saturday night.
He would not confirm what was left at her room in the backpackers, but said her belongings remained there.
More than 20 police staff are on the case, he said.
Police would not comment on her bank account or cellphone activity.
"The longer this goes on, the more worrying it is. At this stage we're hopeful we will find Grace," Det Insp Beard said.
He said police were still trying to get in touch with a number of people she had been with on Saturday night.
Ms Millane's father, millionaire property developer David Millane, is due to arrive in Auckland today.
Det Insp Beard said having him here would allow officers to get to know more about Ms Millane's background.
Her brother, Michael, posted on social media that the family had been calling his sister's cellphone, but that it was going straight to voicemail.
"She spoke to someone in the family every day on WhatsApp, Facebook or FaceTime. The contact with us stopped on Thursday.
"The last contact she had was with her room-mate on Saturday morning.
"Her disappearance was completely out of the blue.''