The prime minister spoke after the white supremacist accused of gunning down 50 people at two mosques in Christchurch dismissed his lawyer and opted to represent himself at trial.
"I agree that it is absolutely something that we need to acknowledge, and do what we can to prevent the notoriety that this individual seeks," Jacinda Ardern told reporters before addressing parliament.
Asked if she would like the trial to occur behind closed doors, she said that was not her decision to make.
The gunman's desire for infamy was made clear by the fact that he left behind a convoluted 74-page manifesto before Friday's massacre and livestreamed footage of his attack on the Al Noor mosque.
That video prompted widespread revulsion and condemnation.
Facebook said it removed 1.5 million versions of the video during the first 24 hours after the massacre.
But on Tuesday, Ardern expressed frustration that the video remained available online, four days after the attack.
She said she had received "some communication" from Facebook's Chief Operating Officer Sheryl Sandberg on the issue.
The prime minister also spoke with British Prime Minister Theresa May about the importance of a global effort to clamp down on the distribution of such material.
Ardern, who spoke on television soon after attack said it was an "extraordinary and unprecedented act of violence". Multiple fatalities were inflicted at two mosques in Christchurch when at least one gunman opened fire on worshippers.
Witnesses told media that a man dressed in a military-style, camouflage outfit, and carrying an automatic rifle had started randomly shooting people in the Al Noor mosque.
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