The man accused of shooting dead 51 Muslim worshippers in the Christchurch mosque attacks has pleaded not guilty to multiple murder and terrorism charges.

Appearing in Christchurch High Court via audio-visual link from a maximum-security prison in Auckland, Brenton Tarrant sat silently as lawyer Shane Tait said his client pleaded "not guilty to all charges". 

The self-proclaimed white supremacist has been charged with 51 counts of murder, 40 of attempted murder and engaging in a terrorist act over the 15 March atrocity.

The 28-year-old Australian allegedly opened fire in the packed Al Noor mosque during Friday prayers and then travelled across town to continue the attack in the suburban Linwood mosque.

The court heard that mental health assessments had found the accused was fit to stand trial for the worst massacre in modern New Zealand history.

About 80 survivors and relatives of those killed packed into the courthouse's public gallery.

Judge Cameron Mander set a trial date of 4 May next year.

Brenton Tarrant was remanded in custody to appear for a case review hearing to be held on 15 August.

The judge barred news outlets from taking photographs or video of his appearance, although he said images from an earlier hearing in April could be used.

New Zealand's government tightened the country's gun laws in the wake of the attack and has said it will review laws dealing with hate speech. 

It has also supported international efforts to ensure that social media giants to do more to combat online extremism.