Grace Millane's father is said to be on his way to the country, where his 22-year-old daughter vanished on Saturday.
She has not returned to her Auckland hostel in several days. Her birthday was on Sunday and police said it was unusual for her not to contact her family then.
Miss Millane, from Essex, was last seen at Auckland's Sky City complex and did not respond to messages on her birthday the following day.
They said Miss Millane had booked to stay at the Base Backpackers hostel in central Auckland until 8 December.
Relatives have shared appeals for information on Facebook, and DI Beard said more than 20 investigators were combing through CCTV footage to track Ms Millane's last movements after a number of unconfirmed sightings had been reported.
Can everyone please share this, we haven't heard from my sister since Saturday is now travelling in New Zealand and was last seen in Auckland.
The witness said the young woman, who she believes to have been Millane, did not have her arm out with her thumb stuck up in the air like a hitchhiker.
Various sightings have her wearing either black top, blues jeans and red sneakers, or a black dress with white shoes.
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