They had previously been speaking with him over the disappearance.
New Zealand police confirmed on Saturday afternoon they are treating the investigation as a homicide.
Scott Beard, the Auckland Police's detective inspector, said he could not confirm if Millane left the hotel.
Grace Millane's family say they are staying positive and hope she returns home soon.
Mr Millane said her family are all "extremely upset" and appealed for the public's help in finding his daughter.
Millane and the man being interviewed by police were together on Saturday evening and went to a number of places before going into CityLife Hotel.
Police later said they had spoken to the man and that he was a "person of interest".
The last confirmed sighting of Millane was at the CityLife Hotel, in Queen St, at 9.41pm on Saturday.
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"Sadly the evidence we have gathered to this point of the inquiry has established that this is a homicide".
"Grace is still missing and we want to find her", he added.
"We still do no know where Grace is".
(AAP) Missing British backpacker Grace Millane has been murdered, police in New Zealand say.
Meanwhile, the scene examination at the Citylife hotel is continuing as detectives review hundreds of hours of CCTV footage.
'Several of her belongings, including her passport, are missing and police believe it is likely Grace has these items with her'.
Police have not yet found the body of the 22-year-old from Wickford in Essex.
They urged members of the public to come forward with any information.
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Late this afternoon police announced they were questioning a man about the murder of Grace Millane, 22, who was last seen in Auckland's CBD a week ago.
Ms Millane was in New Zealand on a gap year, having arrived in the country on November 20.
That was especially so for David Millane, as police had met the distraught father, but also for other family in the United Kingdom, including Millane's mother Gillian, unable to travel to New Zealand because she was recovering from an operation.
"Grace is a lovely, outgoing, fun-loving, family-orientated daughter", Mr Millane said on Friday.
An emotional Beard said it had been a tough time for all involved in the investigation.
"Her family are devastated", he said.
A spokesman for the Foreign Office said: "We are providing consular support to the family in the United Kingdom, and working with the New Zealand Police in relation to reports of a missing British national in New Zealand".
Anyone with information about the missing items has been advised to contact 0800 676 255.
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Millane, the daughter of English property developer David Millane, had not been seen since leaving her hostel in Auckland last Saturday.