At least 49 people were killed in mass shootings at two mosques during midday prayers on Friday and dozens more were wounded, some critically.
Ardern said Tarrant was a licensed gun owner who bought the five guns used in the crimes legally. The Bangladesh team was on its way to the mosque, one of two sites of the shooting attack that killed at least 49 people.
Ardern stressed that families that lost a loved one - particularly if they were dependent on the victim - will receive financial support.
She said this would be looked at as the Government moved to change gun laws but there were a "raft of issues" to look at. Another two individuals are still in custody as the police continue to determine if they were involved in any way.
Police were able to neutralize two devices: an improvised explosive device at one of the mosques and another device found in the suspect's vehicle, which was also rendered safe.
Prime Minister Jacinda Ardern described the tragedy as a "terrorist attack" and noted numerous victims could be migrants or refugees.
Of the four people police apprehended on Friday, one was released ― an innocent bystander who "was just trying to get their kids home", Bush said.
The Associated Press news agency on Saturday reported about an Indian couple in Christchurch looking for their son, Imran Khokhur, who has been missing since the massacre. Police said more charges would follow.
Commissioner Mike Bush hailed the "absolute bravery" of both police and members of the public "who put themselves in harm's way" to apprehend the suspect.
Speaking to media in Wellington earlier, Ardern stressed that "now was the time for change".
She was yet to meet the officers, but had asked after them while meeting with police bosses in Christchurch today and requested that they pass on the "thanks of all New Zealanders".
He appeared in Christchurch court on Saturday where he faced one charge before he was remanded in custody.
At least one of the weapons used by Tarrant was reportedly an AR-15 - the same semi-automatic rifle used in a number of mass shootings in the United States, including the 2012 Sandy Hook school killings in CT.
In what appeared to be the worst attack against Muslims in a western country, witnesses spoke of victims being shot at close range, with women and children believed to be among those killed. She said authorities were working to ensure that bodies could be identified and repatriated quickly to allow for proper Muslim burials.
"There is a dimming of enlightenment in many parts of the world", Parker said. He had no criminal history in New Zealand or Australia and had not drawn the attention of the intelligence community for extremist views.
"President Trump said in the Oval Office a few minutes ago that he did not think white supremacy worldwide was a problem that was rising in any way".