“He sought many things from his act of terror, but one was notoriety – that is why you will never hear me mention his name,” Ms Ardern said in an emotional address at New Zealand’s parliament.
Last Friday’s shootings at two mosques left 50 people dead and dozens wounded.
Australian Brenton Tarrant, 28, a self-described white supremacist, has been charged with murder.
What did the PM say in parliament?
The prime minister addressed a special meeting of parliament on Tuesday, opening her speech by using the Arabic greeting “Al-Salaam Alaikum”, which in English means “peace be upon you”.
She said: “I implore you, speak the names of those who were lost rather than the name of the man who took them. He is a terrorist. He is a criminal. He is an extremist. But he will, when I speak, be nameless.”
Ms Ardern assured MPs that the attacker would “face the full force of the law”. She encouraged New Zealanders to acknowledge the grief of the Muslim community this Friday – which is the Muslim day of worship and will mark one week since the shooting.
Ms Ardern has already announced that the nation’s gun laws will be reformed and that the details would be presented within days.
The prime minister also called on social media platforms to do more to combat terror, after the gunman in Christchurch live-streamed his attack on Facebook.
“We cannot simply sit back and accept that these platforms just exist and that what is said on them is not the responsibility of the place where they are published,” she said. “They are the publisher. Not just the postman. There cannot be a case of all profit no responsibility.”