Ardern has said she supports a ban on semi-automatic weapons and that cabinet has made in-principle decisions to change gun laws which she will announce next Monday.
Ardern, the youthful premier who has become the face of the nation's tragedy, said there would be an inquiry into the horrifying attack, as questions swirl over whether intelligence agencies should have spotted warning signs.
On Monday, Tarrant's lawyer said his client was not mentally unstale and planned to represent himself in the court.
"We detected nothing extraordinary about the licence holder".
New Zealand Police Commissioner Mike Bush says Tarrant acted alone but may have had support.
"The MSSA, military-style automatic, reportedly used by the alleged gunman was not purchased from Gun City".
It was not clear if any of the firearms Tarrant purchased from Gun City were used in Friday's shootings.
The deadly massacre has sent shockwaves across the world - and a call for gun laws in New Zealand to be changed.
Gun City has been criticised for leaving out a roadside advertising billboard that shows a parent helping children with rifle target practice in the wake of the shootings.
"I agree that it is absolutely something that we need to acknowledge, and do what we can to prevent the notoriety that this individual seeks", Prime Minister Jacinda Ardern told reporters.
A bill already before Senate would, among other things, expand the scope of background checks on those who want to acquire guns here.
Under New Zealand law, a trial is "to determine innocence or guilt", Peters said.
Australian Brenton Tarrant, 28, was captured by police and has been charged with one count of murder, but Ardern assured parliament other charges would follow.
They said the family of the Australian man arrested in Christchurch over the shootings were assisting police.
Sarah Liddell, 17, said many of her peers felt intense anxiety since the attack.
Mr Peters told 9News that Tarrant appeared "lucid" and "seemed to appreciate what he was facing and why he was there".
Kawthar Abulaban, 54, who survived the shooting at the Al Noor mosque, came to the cemetery to see the preparations.
"I will not change my opinion about New Zealand".
Ardern has announced that New Zealand will hold a national commemoration service to mark the attack.
Facebook said it removed 1.5 million videos of the shootings during the first 24 hours after the massacre.
Hati Mohemmed Daoud Nabi, 71, opened the door to the Al-Noor mosque.
Muslim leaders conveyed messages of love, compassion and appreciation for the community support they had received.
"Our letters had to recognise all those who have been affected by this senseless act of terror".