Brenton Tarrant, who was last year sentenced to life imprisonment for 51 murders, will represent himself in a hearing in Auckland on Thursday.

The hearing is not an appeal to that sentence, and will not have bearing on the Australian's jail term, which he is serving without the possibility of parole.

Rather, the 30-year-old is asking the court to consider his prison conditions, and, possibly, his designation as a "terrorist entity" by the New Zealand government.

Tarrant is being housed at an Auckland jail, with strict conditions surrounding his imprisonment, and few lines of communication to the outside world.

Last month, the NZ Herald reported a "prison within a prison" known as the Prisoners of Extreme Risk Unit, was housing the Grafton-raised terrorist.

The unit is also housing two other prisoners, and cost $NZ2.8 million ($A2.6 million) in the nine months to October 31.

On Thursday, Tarrant will represent himself at a judicial review, which looks at whether decisions have been made appropriately within the law.

Justice Geoffrey Venning is scheduled to hear Tarrant's case, which will be held over an audio-link, with Tarrant not physically attending the court.

The hearing will be not be open to the public, though media will be permitted to attend.

Given the sensitivities involved with New Zealand's worst modern-day mass shooting, victims of Tarrant's attack were notified prior to the court hearing being listed.

Earlier on Wednesday, New Zealand Prime Minister Jacinda Ardern announced plans to hold another international summit with like-minded countries to eliminate online extremism.

With French President Emmanuel Macron, Ms Ardern launched the "Christchurch Call" in the aftermath of the 2019 attacks, an international agreement between countries and tech giants.

Ms Ardern said the Call had governments, companies and civil society groups "working together in ways that they were not before".

"After the 15 March terrorist attacks, New Zealand said that what happened here should not happen anywhere else and I'm encouraged by the progress made since the atrocities committed in 2019," Ms Ardern said.

A stocktake report, published on Wednesday, said the livestream of the attacks has been viewed millions of times on the internet.

Ms Ardern said "really good progress" had been made towards ensuring tech companies respond quickly to new distressing incidents.

"We have not seen that kind of rapid proliferation of that kind of content online since March 15," she told Radio NZ.

Australian Associated Press