The Prime Minister is continuing to not speak the alleged Christchurch mosque shooter's name and says he "needs to be stopped" from "spreading his hate".
Jacinda Ardern's comments follow revelations from the Corrections Minister, Kelvin Davis, that Australian Brenton Tarrant - accused of murdering 51 people - was able to send seven letters from prison, two to his mother.
Corrections has apologised for allowing the letters to get through. One letter from Tarrant, Newshub revealed, was six-pages long, sent to a supporter believed to be in Russia.
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A copy of the letter appeared on /pol/, a 4chan thread. Much of it appeared innocuous, but it ended with what was effectively a call to action for like-minded people.
"Based on what has happened, based on the ability of the alleged terrorist to be able to communicate in that way, it was entirely right that Corrections [apologised]," Ardern told media in Tuvalu.
"No one wants extra trauma for the victims, extra trauma for Christchurch, and ultimately no one wants this alleged offender to be able to spread his message of hate in the way that he's been able to."
The Prime Minister vowed not to speak Tarrant's name following the March 15 Christchurch terror attacks. In a speech to Parliament on March 19, she said: "You will never hear me mention his name."
Ardern told media in Tuvalu that there had "clearly" been a "systemic failure" in that Tarrant was able to send letters to his supporters.
"Now we have to make sure that the department is going back and checking their systems, and equally that we're checking the law."
The Corrections Act states that a prison manager may withhold mail between a prisoner and another person if it could "endanger the safety or welfare of any person".
Massey University law professor Chris Gallavin told The AM Show there's nothing wrong with the current law around prison mail and pointed blame at Corrections' "stuff-up".
"If he wants to write to his mother or his parents about things that are completely innocuous, then we should absolutely let him. He has some rights and they're there for a good reason," he said.
"What he can't do is have a platform and stage to spew his vitriol or promote criminal activity."
Since the Corrections Minister announced that Tarrant's mail privileges have been suspended for the foreseeable future, his supporters have been rallying online demanding they be reinstated.
The alleged shooter's ability to send letters has raised concerns about his influence, since several deadly copycat shootings have happened since March 15, with multiple suspects citing Tarrant as their inspiration.
"If there are any holes here that need to be fixed, that needs to be rectified immediately," Ardern said. "This will be an individual who continues to try and spread his hate and that needs to be stopped."
National's Corrections spokesperson David Bennett is calling for the Corrections Minister to resign.