Watch: Prime Minister Jacinda Ardern chokes up while apologising to Grace Millane's family

Prime Minister Jacinda Ardern issued an emotional apology to the family of murdered tourist Grace Millane.

She addressed the 22-year-old's death first thing in her post-Cabinet press conference on Monday.

"I cannot imagine the grief of her family and what they would be experiencing and feeling right now," she said.

"My thoughts and prayers are with her father David, who is in the country, her mother Jillian, who cannot be here, and her wider family, 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 to those who are visiting our shores.

"So on behalf of New Zealand, I want to apologise to Grace's family," she said before pausing and looking down.

"Your daughter should have been safe here, and she wasn't, and I'm sorry for that," she continued, with an audible catch in her throat, seemingly near tears.

"I've advised the family through the police that if there is anything we can do to assist, we are here to help with that."

Ms Millane was visiting New Zealand during a year-long OE. She was reported missing on Wednesday, December 5, and on Sunday police found a body in the Waitākere Ranges which is believed to be that of Ms Millane.

A 26-year-old man has been charged with her murder.