"Grace has been missing for five days", he wrote.
Police would not comment on her bank account or cellphone activity.
On Wednesday, police received a missing person's report regarding the English national, who is now visiting New Zealand on holiday. "At this stage we're still hopeful that we'll find Grace".
It has since been revealed that Grace Millane, who has been in New Zealand for about two weeks, is the daughter of a millionaire property developer, David Millane, the Daily Mail reported.
Her family in the United Kingdom raised the alarm on Monday and Detective Inspector Scott Beard said her disappearance was "out of character".
Detectives are investigating the disappearance of 22-year-old Grace Millane, who was last seen in Auckland on Saturday night.
Ms Millane's roommates at Base Backpackers Hostel, on Queen Street, in the heart of Auckland, said they last saw her on Saturday.
She was due to leave New Zealand in about two weeks, police said.
"We are asking anybody who has been in contact with her or knows her to contact police".
Beard said having him here would allow officers to get to know more about Grace Millane's background.
She had travelled to the Bay of Islands on a trip, then arrived in Auckland on Friday.
Australia to meet the Kohli threat full (length) on
India off-spinner Ravichandran Ashwin may remember a similar schooling the last time the Test team toured Australia in 2014/15. Paine reiterated his confidence that a four-bowler attack would be good enough to see Australia through this first Test.
Wolves come from behind to beat wasteful Chelsea
It lifted Wolves up to 12th and was their first win for two months after five defeats in their previous six games. I am really anxious not for the result but for the fact that we didn't react to the first goal of the opponent".
Nations pressed on 'urgent threat' of climate change
Citing a recent scientific report, the United Nations chief urged governments to aim for net zero emissions by 2050. Attenborough's speech comes at a crossroad for global climate action.
Grace Millane had been in New Zealand for about two weeks.
They became anxious when she failed to contact them on her birthday...
While she was travelling alone, Michael Millane said she had made a lot of friends.
New details have emerged about the background of a missing British backpacker and her time in New Zealand.
Thousands of people have shared the post.
Ms Millane is about 5ft 6in tall with brown hair and brown eyes.
A spokesman for the Foreign Office said it is providing consular support to the family in the UK.
"In the CCTV image Grace is seen wearing a black dress and white shoes, believed to be Converse shoes".
"We are working closely with her family at this time and a number of Police staff are now working on this matter".
A missing person report was received on Wednesday for the 22-year-old after her family had not heard from her for several days.
"She hasn't really replied to any messages between the family and it was her birthday on Sunday and she didn't respond to any messages".