On Saturday, officers said that the 26-year-old man - who had been speaking to them in relation to Grace's disappearance - is to be charged with her murder.
They revealed yesterday that their investigations included questioning the man with Millane when she was last seen.
"The family is devastated, everybody who is a parent out there will understand what this family is going through". "We are all extremely upset, and it's very hard at this time to fully describe the range of emotions we are going through".
He also added that Millane's current whereabouts remain unknown, and that the police are "determined to find her and return her to her family".
On Saturday police released images of her necklace and watch and urged anyone who recognised the items to come forward.
After visiting Peru she arrived in New Zealand on November 20 and had been near-daily contact with her family until December 1 - the day before her 22nd birthday.
Grace Millane, 22, was last seen a week ago entering an inner-city hotel in Auckland with a man.
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"A 26-year-old man was located at a central Auckland address by police".
Grace Millane, 22, went missing in Auckland, New Zealand, on December 1.
A auto seized in relation to Millane's disappearance, meanwhile, appears to be the key piece of evidence in her death, a former police inspector says.
A statement posted on Facebook by the Millane family described her as "a fun-loving, outgoing and family-orientated person".
Police investigating the murder of British tourist Grace Millane have cordoned off what appears to be a crime scene along a section of Scenic Drive in the Waitakere Ranges. "Grace has never been out of contact for this amount of time".
Police said she was seen the same day leaving an Auckland hotel with a "male companion".
"Many of these calls have been from members of the public, offering accommodation and assistance to the Millane family".