At the start of this morning's hearing in the Auckland District Court, Judge Evangelos Thomas addressed members of Ms Millane's family.
"Before we call this matter I'd like to acknowledge the presence of Grace's family. I don't know what we say to you at this time. Your grief must be desperate," Judge Thomas said.
"All of us hope that justice for Grace is fair, swift and ultimately brings you some peace. That will not be happening today. There will be no judgement today. It is important there is no judgement today.
"There will be in all likelihood a number of procedural issues we need to deal with today. Those are all part and parcel of a process that has judgement as its end goal, not its starting point."
The 26-year-old accused of murdering Ms Millane between 1 and 2 of December appeared this morning dressed in a blue boiler suit.
The court heard extensive submissions on interim name suppression, but Judge Thomas declined to grant it.
The accused's lawyer Ian Brookie indicated he would appeal, prohibiting media from identifying the accused in the meantime.
As the accused was walked out of court, a person in the public gallery yelled "Scumbag".
He has been remanded in custody until he appears in court in January.
Ms Millane's body was discovered yesterday afternoon, in an area of bush just 10 metres off the road, in Auckland's Waitakere Ranges.
The body has been removed the scene and is yet to be formally identified, but police believe it is the backpacker.
One of Ms Millane's brothers has paid tribute to his sister, posting a series of photos of himself with her online, captioned with the lyrics to the song You Are My Sunshine.
Declan Millane's tribute joined a stream of others online, including from the University of Lincoln where Ms Millane had graduated before heading off to travel the world.
Detective Inspector Scott Beard said the police investigation into Ms Millane's death would continue for some time, as they pieced together what happened after she was last seen entering a central Auckland hotel more than a week ago.
They want to hear about any sightings of a 2016 red Toyota Corolla rental car last Monday morning in West Auckland.
The car was rented in central Auckland and was then found in Taupo.
Ms Millane, who went missing on the eve of her 22nd birthday, was last seen last Saturday night going into CityLife Hotel with a man.
Support has been given to Ms Millane's father, David Millane, who travelled to New Zealand following his daughter's disappearance and remains in the country with his brother, who is also from England.