Meanwhile, preparations were underway for a massive Friday prayer service to be led by the imam of one of the two New Zealand mosques where worshippers were killed.
The refugee family moved to New Zealand past year, finally settling in a safe haven, after fleeing Syria and spending time in Jordan. About 10 of them were in critical condition, including a 4-year-old girl.
On March 15, 50 Muslims were killed at two Christchurch mosques during a terrorist attack while they were attending Friday prayer.
She also said that she needed answers from social media giants, especially Facebook where the video of the shooting was viewed around 200 times, but had managed to be circulated 1.5 million times, as to how they did not think of blocking the footage.
Mr Javed Dadabhai, who travelled from Auckland to help bury his cousin, said families and volunteers were told "it is going to be a very slow process, a very thorough process".
"I implore you: Speak the names of those who were lost, rather than the name of the man who took them", Ardern told the press.
In the meantime she encouraged people with guns they were concerned about to surrender them to police, which they could do at any time.
The scale of the attack has caused global revulsion, including for Tarrant's use of social media to livestream the carnage in real-time.
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Ms Ardern has said details of the government's proposed law changes on gun ownership will be announced by next week, but she indicated gun buybacks and a ban on some semi-automatic rifles were under consideration.
Ardern's announcement comes less than a week after the killings, as more of the dead were being buried. "Our actions, on behalf of all New Zealanders, are directed at making sure this never happens again".
She also instituted a mandatory buyback program, in acknowledgment that many such weapons now exist.
Islamic funerals are traditionally held as soon as possible, usually within a day.
Australian Brenton Tarrant, 28, a white supremacist who was living in Dunedin, on New Zealand's South Island, has been charged with murder following the attack. Police Commissioner Mike Bush said authorities have formally identified and released the remains of 21 victims. She knelt amid the flowers and wept, grabbing at daisies and lilies as though she might find her boy in them.
"Within 10 days of this horrific act of terrorism we will have announced moves which I believe will make our community safer", she said.