"I want to reassure the public police are determined to do everything we can to find her".
"Just after 3pm this afternoon a 26-year-old man was located at a central Auckland address by police", Detective Inspector Scott Beard told media.
"We still don't know where Grace is", Beard said, who added police have identified a vehicle of interest today.
Ms Millane, 22, from Essex, England, was last seen at an Auckland hotel almost a week ago.
Miss Millane's body has not yet been found, but Det Insp Beard said police were "determined to do all we can to find her".
He added the "thoughts of all New Zealanders will be with Grace's family tonight".
She was in New Zealand as part of a year-long trip around the world, having started in Peru, then arrived in New Zealand on November 20.
Searches have also been carried out at the backpackers' accommodation where she was staying.
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.
Investigators had said yesterday that they held "grave fears" for Grace's safety.
"Somebody may find it somewhere, we don't know what has happened to it".
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Beard said Millane had been out of contact with her parents for days and, especially worrying to her family, they weren't able to contact her on Sunday for her 22nd birthday.
Millane had been in New Zealand for two weeks, the UK's Press Association news agency reported.
Police had spoken to Millane's family this afternoon, Beard said.
Meanwhile, the scene examination at the Citylife hotel is continuing as detectives review hundreds of hours of CCTV footage.
Her father, David Millane, said they last had contact on the day she vanished.
'Several of her belongings, including her passport, are missing and police believe it is likely Grace has these items with her'.
Images of her pale pink watch and silver necklace were released by police after it was noted they were missing from her belongings at the backpackers' hostel where she was staying.
They urged members of the public to come forward with any information.
Police have no evidence to suggest the pair knew each other before December 1, Inspector Beard said.
"There is family back in the United Kingdom and our hearts go out to them as well".
Anyone with information that could help with the investigation has been asked to contact 0800 676 255.