David Millane said his family was “extremely concerned” for the welfare of his “fun-loving” daughter Grace Millane, who turned 22 on Sunday, following her disappearance nearly a week ago.
The tourist, from Essex, was on a year-long round-the-world trip.
She had been “bombarding” her loved ones with messages and pictures from her adventure.
But they became concerned when contact with Ms Millane went cold. She was last seen in Auckland at 9:41pm at the Citylife Hotel on 1 December with a “male companion”.
During an emotional press conference in Auckland, Mr Millane said: “Grace has been missing for seven days.
“We last had contact with her on Saturday 1 December and as a family we have been extremely concerned for her welfare.
“Grace is a lovely, outgoing, fun-loving, family-orientated daughter.
“Grace has never been out of contact for this amount of time.
“She’s usually in daily contact with either her mother, myself, her two brothers or members of the family on social media.”
Detective Inspector Scott Beard, from Auckland City Police, said officers had identified and spoken to the “male companion” last seen with Ms Millane.
Mr Beard said officers had also identified an apartment at the city centre hotel as a location of interest.
“It has now been six days since Grace was last seen,” he said. “At this point, we hold grave fears for her safety.”
He added they “still have no evidence of foul play”.
Mr Millane arrived in New Zealand this morning. He told reporters it was unusual for his daughter to be out of contact.
Mr Millane said: “She has been bombarding us with numerous photographs and messages of her adventures.
“We are all extremely upset and it’s very difficult at this time to fully describe the range of emotions we are going through.
“Finally, I would like to take this opportunity to appeal to anybody who has seen, spoken to, come into contact with Grace over the last few days and come forward with any detail, no matter how small.”
Ms Millane arrived in New Zealand on 20 November, having previously visited Peru.
Her last Twitter post appears to be on 30 November – the day before she was last seen.
Police said more than 25 staff were working on the case and were trawling through hours of CCTV footage to trace her movements.
A spokesman for the Foreign Office said: “We are providing consular support to the family in the UK, and working with the New Zealand Police in relation to reports of a missing British national in New Zealand.”