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Millane had been travelling around New Zealand as part of a year-long OE. Her body has been recovered and a man charged with her murder.
Speaking at her post-Cabinet press conference today, Ardern said the murder was a tragedy.
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"On behalf of New Zealand, I would like to apologise to Grace's family, your daughter should have been safe here and she wasn't and I'm sorry for that," Ardern said.
"I cannot imagine the grief of her family and what they would be experiencing and feeling right now. My thoughts and prayers are with her father David who is in the country, her mother Gillian who cannot be here, and her wider family and friends and loved ones.
"From the Kiwis I have spoken to, there is this overwhelming sense of hurt and shame that this has happened in our country, a place that prides itself on our hospitality, on our manaakitanga, especially those visiting our shores.
"On behalf of New Zealand, I want to apologise to Grace's family."
Her voice cracking, Ardern said: "Your daughter should have been safe here, and she wasn't, and I'm sorry for that."
Ardern said that it was "not necessarily" the Prime Minister's place to apologise on behalf of the country.
"It's just something I sense that New Zealanders may have wanted to convey, and I'm in a position perhaps where I'm able to convey that.
"We pride ourselves on being a place where people are welcome and where they're safe, and that hasn't happened in this case. I feel the sense that New Zealanders found it quite personal."
She acknowledged she also felt the tragedy personally.
"I don't think I'm alone in feeling that way. I think all New Zealanders will just feel their heart breaking for that family."
The alleged killer appeared in Auckland District Court today as a post mortem examination was carried out to establish when and how exactly Millane died.
Millane arrived in Auckland on November 30. The next night she was captured on CCTV footage entering the CityLife hotel in the CBD with a 26-year-old man.
He allegedly murdered Millane some time that night, or the next day - which was her 22nd birthday.
Nine days later her body was found in an area of bush in West Auckland's Waitakere Ranges.
Ardern said she had advised the Millane family through the police that the Government is prepared to do anything that would be of assistance.