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Auckland Mayor Phil Goff says it's frustrating not all the details of the attacker can be revealed because of a court order.
He said he knew nothing about the individual beforehand but added, from his experience in government, the number of people under such level of police surveillance could be counted "on less than the fingers on one hand".
"What's frustrating for all of us who have just listened to the Prime Minister and the police commissioner, is that they were constrained from sharing all of the information that they know about this individual, because of a court order, and I understand that the Prime Minister of all people have to live under the law, and cannot go outside the law.
"But what is clear about it is that this person is an ideologically-motivated terrorist... It's appalling that he could cause so much hurt in the space of a minute, just with a knife. But I guess the police interceded as quickly as they were able and ultimately, he has paid the price of his actions.
"This person, from the information that the Prime Minister has given us, was obviously a hate-filled person whose views were causing huge alarm to the police, but who had not acted in a way that the law enabled him to be kept them custody.
"Now, we're having this bit of this debate a little bit over hate speech at the moment… people saying 'people's views are their views, and they're allowed to express their views'.
"But people like this who obviously expressed views filled with hatred, based on his ideology, the fact that you can't act against them, would seem to be a potential gap in our law."
"I'm sure as well as the Independent Police Complaints Authority Investigation and the Coroner's investigation, Parliament will want to look pretty closely at whether the law is adequate – albeit in a democratic society such as we have – when a person that constitutes a risk so severe that he's kept under 24/7 surveillance, there can't be action against him.
"I think that's going to exercise the minds at Parliament in the months to come."
Goff said he would not expect as mayor to be informed by police about particular individuals that constitute a risk.
"We regrettably have individuals like this and the individual that attacked the mosques in Christchurch. It's not a common activity but when it happens it's shocking for the horror, and most of us just can't understand the venom and the hatred that can be held in a person's mind, that motivates them to act like that.
"But does that mean that all of us are unsafe in our community? No, New Zealand remains one of the safer communities around the world.
"That doesn't mean to say that we shouldn't take every action that we can to try to increase that security and to look at the law where we think the law may not cover a situation where a man is regarded as such a threat, but no action can be taken against him. That's the question I think on all of our minds."