Grace Millane, who is from Essex, has been reported missing by her family, who say they have not heard from her in almost a week.
The 22-year-old was travelling solo through the country, and staying in an Auckland hostel.
She had been in nearly daily contact with her family through social media and WhatsApp messages.
Ms Millane's family, from Wickford, near Basildon, said they had spoken to her "most days" previously on the trip, and that her silence is "completely out of character". "Please share and contact if you have any information regarding her whereabouts".
"Police are aware of a number of reported sightings of Grace from members of the public".
Mr Millane said she graduated from the University of Lincoln in September and planned to travel around the world.
Millane urged anybody who had seen or spoken to his daughter over the past week to contact police.
Millane had reportedly been staying at Base Backpackers in Auckland.
She was wearing a black dress and what are believed to be white Converse trainers.
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He added that she had travelled to Peru as part of an organised group for six weeks but had not travelled on her own until she arrived in New Zealand two weeks ago.
Ms Millane's brother Michael said: "We are really, really anxious and concerned about Grace".
She is about 5ft 6in tall with brown hair and brown eyes.
"We are asking anybody who has been in contact with her or knows her to contact police".
Her family said she had then meant to go to Australia.
Grace Millane had been in New Zealand for about two weeks.
The family put the call out there because they were anxious for her safety and wanted "to make sure she's alright".
While she was travelling alone, Michael Millane said she had made a lot of friends.
Base Backpackers declined to comment to the Herald on Wednesday.
A spokesman for the Foreign Office said it is providing consular support to the family in the UK.