Grace Millane, who turned 22 on Sunday, was last seen entering the CityLife hotel in Auckland at 9:41pm on Saturday 1 December.
Detective Inspector Scott Beard from Auckland Police was unable to confirm on Friday if Ms Millane had left the hotel.
He said: "As part of our investigation we have reviewed hours and hours of CCTV footage and this will continue throughout the weekend."
DI Beard added that Ms Millane, from Wickford, Essex, was with a male companion when she entered the hotel.
He continued: "Police have identified this man and he has been spoken to.
"Through our investigations we have also identified a location of interest as an apartment in the CityLife hotel in Queen Street.
"We are conducting a scene examination at this address."
The police officer said the man is not in custody but is a person of interest in the case.
He said there is no evidence of foul play and that Ms Milane is still being treated as missing, but added: "At this point we hold grave concerns for her safety."
DI Beard would not confirm reports she had been using the dating app Tinder while in Auckland.
Ms Millane's father David has flown out to New Zealand amid the investigation into her disappearance.
He told reporters: "Grace is a lovely, outgoing, fun-loving, family-orientated daughter.
"Grace has never been out of contact for this amount of time.
He added that Ms Millane had been in Peru in South America before arriving in New Zealand alone as part of a year of travelling.
She was staying at the Base Backpackers hostel in central Auckland before her disappearance.
Mr Millane continued: "She had been bombarding us with numerous photographs and messages of her adventures.
"We are all extremely upset and it is very difficult at this time to explain the range of emotions we are going through."
New Zealand police have released a CCTV image of Ms Millane entering the SkyCity entertainment complex at around 7:15pm on Saturday.
She was wearing a black dress and what was believed to be white Converse trainers.
A number of unconfirmed sightings have been reported to officers.