Police say they are questioning a 26-year-old man who was seen with her on the night of her disappearance. "At this point, we hold grave fears for her safety".
The last confirmed sighting of the 22-year-old was at 9.41pm the same day at the Citylife Hotel in central Auckland, when she was seen with a "male companion".
"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.
Mr Beard said Ms Millane's passport, necklace and watch were still missing and police wanted anyone with information on these or anything else to get in touch on 0800 676 255.
Grace Millane had been in New Zealand for about two weeks.
Earlier searches of Millane's accommodation at a backpackers' hostel found several items, including her passport, were missing.
Speaking at a news conference in Auckland on Friday, Grace's father, David Millane, said his daughter had been "bombarding us with numerous photographs and messages of her adventures" before she went missing.
An emotional Beard said it had been a tough time for all involved in the investigation.
The graduate's birthday was on Sunday but she did not contact her family.
Police continue to offer support to the Millane family, both in New Zealand and in the UK.
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At a press conference at 5pm local time, Det Insp Beard told reporters Ms Millane's family had been informed of the investigation's latest development.
On Saturday police released images of a pink watch and a necklace belonging to her and asked for the public's help in finding them.
Police have been conducting a scene examination at a unit in the hotel. "This issue here is Grace is still missing and we want to find her".
Beard said "that property is going to be somewhere, the clothing is going to be somewhere, we haven't found it".
A tearful David Millane appealed to the public to come forward with any information, "no matter how small".
Beard wouldn't say whether police had seen footage of the man leaving CityLife Hotel or if he thought Millane was killed in the hotel, a large apartment-style complex.
"We've spoken to David [Grace's father] we've met him, but there is family in the United Kingdom and our hearts go out to them as well".
This was her first time travelling overseas alone.
"Everybody who is a parent will understand what the family is going through. our hearts go out to them".