New South Wales native Tarrant stands accused of shooting almost 100 worshippers at the Al Noor and Linwood mosques in central Christchurch on March 15.
Tarrant live streamed the massacre on Facebook via body cam.
He was initially arrested on one count of murder.
Presiding Justice Cameron Mander has declined 12 applications from domestic and international media outlets to film or audio record inside the courtroom on Friday, citing the need to ensure due process, judicial integrity and a fair trial.
During his last court appearance one day after the massacre, a handcuffed Tarrant made a white supremacist gesture and smirked to those present.