'We last had contact with her on Saturday the 1st of December and as a family we've been extremely concerned for her welfare, ' said Mr Millane, who arrived in New Zealand on Friday morning. "At this point, we hold grave fears for her safety".
He added the "thoughts of all New Zealanders will be with Grace's family tonight".
A 26-year-old man is now being held in connection with the murder, Det Insp Beard added.
"I want to reassure everyone, both here and overseas, that New Zealand Police are determined to do everything we can to find her".
"Dozens of calls have been made to the 0800 number and all of this information continues to be reviewed and assessed".
"Of course it's tough, everyone who is a parent out there will understand and appreciate what that family is going through", Beard said.
The revelation follows a forensic examination of a hotel where she was last seen on Saturday 1 December with a "male companion".
Det Insp Beard confirmed that the man being questioned by police on Saturday was the same individual.
The last confirmed sighting of Grace is still 9.41pm Saturday night going into the CityLife Hotel, Beard said.
Police have not uncovered any evidence the pair had met before. "This issue here is Grace is still missing and we want to find her".
A vehicle of interest had been secured and police were trying to find out exactly where the vehicle had been since Millane's disappearance.
Grace Millane’s father David Millane spoke to reporters on Friday Dec. 7 2018
Earlier in the day police released photographs of a necklace and a watch in the hopes of finding her whereabouts.
Miss Millane, who graduated from the University of Lincoln in September, had been travelling alone in New Zealand for two weeks, following a six-week group trip through South America.
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.
Millane, the daughter of English property developer David Millane, had not been seen since leaving her hostel in Auckland last Saturday.
'We're all extremely upset and it's very hard at this time to describe the range of emotions we are going through'.
'Grace is a lovely, outgoing, fun-loving and family orientated daughter'.
The graduate's birthday was on Sunday but she did not contact her family.
Auckland City Police said it received a missing person's report on Wednesday.
Her brother, Michael Millane, said the family began getting anxious on Monday when she did not reply to messages.
"I would just like to take this opportunity to appeal to anybody who has seen, spoken to, or come into contact with Grace over the last few days, to come forward with any detail, no matter how small, and contact the investigation team", he said.
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