Mr Millane expressed gratitude to police and said he hoped that the murder would not prevent people from exploring the world.
“Grace was not born here and only managed to stay a few weeks, but you have taken her to your hearts and in some small way she will forever be a Kiwi,” Mr Millane said in a statement last month. “We all hope that what has happened to Grace will not deter even one person from venturing out into the world.”
The murder prompted vigils across New Zealand to express support for the Millane family and to protest violence against women in New Zealand and around the world.
New Zealand Prime Minister Jacinda Ardern last month issued an emotive public apology to Ms Millane’s family.
“Your daughter should have been safe here and she wasn’t and I’m sorry for that,” she said.
At the court in Auckland, Justice Simon Moore ordered the accused to be kept in custody. The trial is expected to last three weeks.
The judge repeated calls for the media and the public to honour the court’s order that the accused’s name be suppressed.
The accused will next appear in court on April 3.