The victims of Friday's shooting included immigrants from Jordan, Saudi Arabia, Turkey, Indonesia, and Malaysia.
She said neither the gunmen nor the suspected accomplices were on any terrorist watchlist in New Zealand or Australia.
It is customary in Islam to bury the dead within the 24 hours.
The video footage showed a man driving to the mosque, entering it and shooting randomly at people inside.
After Tarrant left, the judge said that while "there is one charge of murder brought at the moment, it is reasonable to assume that there will be others".
Among the wounded, two were in critical condition, including a four-year-old child, said Police Commissioner Mike Bush.
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. Gunmen opened fire in two separate mosques in Christchurch on Friday, killing 49 people and wounding 48 others.
They shared a video message from musicians SOL3MIO, who dedicated a song to "New Zealand, and to family and friends". "That obviously leads to an Australian-based investigation and all of our inquiries here will be absolutely shared and communicated with New Zealand authorities".
"As soon as New Zealanders hear that someone was legally able to acquire, as I'm advised, those weapons and carry out this event, that will raise enormous questions with our gun laws, and that is why we will respond swiftly", Ardern said of the situation at her press conference.
"I can tell you one thing right now, our gun laws will change", Ardern said adding that a ban on semi-automatic weapons would be considered.
The suspect had five guns with him during the attack, described by multiple media outlets as "two semi-automatic weapons, two shotguns, and one lever-action firearm". Police say that this person was a member of the public armed with a gun with the intention of assisting officers. Tarrant did not apply for bail, and per ABC News reports, did not apply to have his name suppressed. The minimum legal age to own a gun in New Zealand is 16, or 18 for military-style semi-automatic weapons. Three people are in custody over the mass shootings.
Sanjiv Kohli, the Indian diplomat, tweeted after the attack on Friday: "As per updates received from multiple sources there are 9 missing persons of Indian nationality/origin". Police told her that he is not among the 49 fatalities.
Pence also affirmed USA cooperation in ensuring all the perpetrators were brought to justice. "These acts of hate have no place in the diverse and tolerant society for which New Zealand is justly known", the White House statement said.