Meanwhile, her father had made a decision to fly to Auckland from Essex, in southeast England, on Wednesday night (England time) and was due to arrive in New Zealand on Friday.
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.
Detective Inspector Scott Beard said: 'Clearly this is a very stressful time for Grace's family and the longer she remains missing the more our concern grows for her safety and wellbeing.
Before New Zealand she had spent four weeks travelling in South America.
"We have her on CCTV footage at 7.15pm on Saturday night, from where she went there, we don't know, but obviously that's part of our investigation".More news: Tom Cruise's Impassioned Twitter Plea May Solve A Common Problem
Her brother, Michael Millane, told Sky News the last person to speak to his sister was their mother last Thursday, and that not hearing anything from her was unusual.
She could not remember if the young woman had bags with her or not or whether she saw the woman standing by the road on Friday or Monday afternoon.
Relatives, who said they spoke to her "most days", became concerned when she failed to reply to birthday messages on Sunday.
Her family in the United Kingdom raised the alarm on Monday and Detective Inspector Scott Beard said her disappearance was "out of character". They're on the other side of the world and they haven't heard from her, ' he said.
"I looked at the photo [of Millane] and I was quite adamant I had seen that girl", she said.More news: HMD announce their next Android One phone the Nokia 8.1
Ms Millane's father, David Millane, 60, a millionaire property developer, is in the process of flying to New Zealand to help with the search.
CCTV and social media is being combed for clues as to her whereabouts.
Ms Millane, an advertising and marketing graduate who graduated from the University of Lincoln previous year, had spent six weeks travelling with an organised group in South America before going to New Zealand alone.
On November 19 she wrote: 'Of course it's raining when I arrive to New Zealand'.
"It's unusual for her not to chat so we're really anxious - this is totally unlike her".More news: Huawei's quickly closing the global phone sales gap to Samsung
She also made money selling paintings which she exhibits on her own website.
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