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He also said New Zealand's security legislation needs to be reassessed with some urgency to ensure "New Zealanders are kept safe".
Speaking to media last Monday, Prime Minister Jacinda Ardern confirmed there would be an official inquiry into specific circumstances leading up to the terror attack.
It would look at what all relevant agencies knew or could or should have known about the individual and his activities, including the alleged gunman's access to weapons and whether they could have been in a position to prevent the attack.
"It would also assess if there were any impediments to the sharing of information, such as legislative or intelligence sharing challenges," Ardern said.
She added the New Zealand SIS, GCSB, Police, Customs, and Immigration's role in response, and leading up to, the shooting would be looked into.
Although a Royal Commission of Inquiry was on the table, Ardern was not able to confirm at the time if that was the route the Government would take.
But Bridges said this was the only suitable level of inquiry available to the Government.
Speaking to the Herald, he said although other inquiries could undertake the review, it wouldn't have the "stature, the independence and the thoroughness of a Royal Commission".
A Royal Commission, Bridges said, would provide an overall sense of confidence for all New Zealanders.
"In light of what has happened, we need that."
New Zealand's security legislation needed to change as well, Bridges said.
Project Speargun – a programme which would have scanned internet traffic coming into New Zealand – was abandoned in 2013 by the then-National Government after "vocal views against it", Bridges said.
He added that this was because many of the critics were prioritising privacy over safety.
He said Speargun would have "given an extended degree of protection to all New Zealanders".
A system called Cortex is now in place in New Zealand, but Bridges said it was much narrower and designed to protect institutions.
He would not, however, say if the Government's decision to abandon the programme was a mistake.
"My view is everything has changed – I'm not pretending it's easy – but where the line is now drawn has to be reconsidered.
"We have seen what ISIS is saying, we have seen the Turkish President playing [footage from] the massacre at rallies, we know there is a risk of copycatting," he said.
"So I think there is some urgency to revisit the legislation and deciding where the line between privacy and safety is – I'm for moving it towards safety."