The 26-year-old man has been speaking with police in Auckland in relation to her disappearance, officers said.
The 26-year-old man who has been speaking with police about the disappearance of British backpacker Grace Millane will be charged with her murder.
"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 NZ Police are determined to do everything we can to find Grace", Beard added.
"We still do not know where Grace is".
The 22-year-old from Essex - described by her father as "lovely" and "family-orientated" - was last seen in New Zealand a week ago.
Grace Millane had been in New Zealand for about two weeks.
Police said they brought that man into the central Auckland police station on Saturday afternoon for questioning.
He wouldn't speculate where Grace was killed, Beard said.
Detectives searching for her said several of her possessions, including her passport, are also missing.
Despite a major police search and public campaign for information, no further sightings of the backpacker have been confirmed.
"Everybody who is a parent will understand what the family is going through. our hearts go out to them".
Millane, 22, went missing from a hostel in Auckland on December 1.
DI Beard confirmed that the man being questioned by police on Saturday was the same individual.
"We know that they were together from the time at the Sky City Hotel".
Police have not uncovered any evidence the pair had met before.
Beard said "that property is going to be somewhere, the clothing is going to be somewhere, we haven't found it".
Detectives seized a "vehicle of interest" on Saturday and inquiries were under way to establish where it had been.
Her passport is also missing.
Police believe they visited a number of locations that evening and are looking for information on where a vehicle identified in the case has been driven.
Police believe Millane may have the items with her.
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.
Five days later, on Friday, David Millane arrived in New Zealand and spoke with media. "Grace has never been out of contact for this amount of time". She was formally reported missing on Wednesday, December 5.
Police had spoken to Millane's family this afternoon, Beard said.
More than 25 Police staff are now working on the investigation into the disappearance.
They are trawling through hours of CCTV footage to trace her movements.
He will remain in Police custody until Monday morning when he will appear in the Auckland District Court.