"We will be looking to move as quickly as we can," Prime Minister Jacinda Ardern told Radio New Zealand. She did not want to pre-empt the Cabinet discussion.
"Certainly though, I can reflect that there will be many New Zealanders who will be asking right now how is it and why is it that someone should be able in New Zealand to acquire a military-style semi-automatic weapon?"
He has been remanded in custody until April 5 and police say he will face further charges.
The Prime Minister said earlier that the accused held a gun licence and seemed to have acquired the guns in the attacks legally.
"One of the issues we are facing is that the guns that were used in this case appear to have been modified," Ms Ardern said.
On Sunday, she confirmed that a white supremacist manifesto thought to be from the accused was sent to her office.
The families of the victims were still waiting to be able to bury their loved ones. Ms Ardern on Sunday said that it was expected that all bodies will be returned to families by Wednesday.
The first funerals are expected to be held on Monday.