The victims of Friday's shooting included immigrants from Jordan, Saudi Arabia, Turkey, Indonesia, and Malaysia.
New Zealand has in the past tried to tighten firearm laws, but a strong gun lobby and culture of hunting has stymied such efforts.
However, because none of the bodies have been returned to the victims' families because of the investigation, many having been unable to bury their dead within the 24 hours customary in Islam.
In the video live-streamed by Tarrant, a man inside a mosque appears to say: "Welcome brother", as a gunman approaches.
Two other people were in custody and police said they were working to understand their involvement.
The death toll in the New Zealand mosque shootings rose to 50 on Sunday after police said they found another body at one of the mosques, while authorities worked to formally identify victims and release their bodies to families.
One of the images most widely shared on social media in solidarity with New Zealand is a cartoon of a kiwi, the country's national bird, crying.
The Christchurch attacker could have killed even more people as he was on the move at the time of his arrest, and had more firearms in his auto, New Zealand's PM said, praising police who responded to the call in just 36 minutes.
"While work is being done as to the chain of events that led to both the holding of this gun license and the possession of these weapons, I can tell you one thing right now: Our gun laws will change", she said at a press conference.
Ardern said the main suspect was a licensed gun owner who used five weapons during his rampage, including two semi-automatic weapons and two shotguns.
In a manifesto circulating online, Tarrant described himself as "Just a ordinary White man, 28 years old" who used the spoils of cryptocurrency trading to finance extensive travels through Europe from 2016-2018. Story continues after video.
The AR-15 is a semi-automatic version of the United States military M16 rifle.
'But the Prime Minister has signaled that we are going to look at that issue [banning semi-automatic weapons]'.
Australia imposed stricter rules on gun control and bought back firearms after a mass shooting left 35 people dead and 23 injured at a cafe in Port Arthur, Tasmania, in 1996. In some ways, it felt like a first - an internet-native mass shooting, conceived and produced entirely within the irony-soaked discourse of modern extremism, a report in New York Times noted. Police told her that he is not among the 49 fatalities.
Pence also affirmed US cooperation in ensuring all the perpetrators were brought to justice.
Western leaders from Donald Trump to Theresa May expressed solidarity with New Zealanders, deploring what the White House called a "vicious act of hate".
49 dead in New Zealand mosque shootings
When asked why they weren't on any lists, Ardern said: "It's an indication they had not acted in a way that warranted it". Australian Prime Minister Scott Morrison on Friday confirmed the attacker at the Masjid al Noor mosque was an Australian.