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National leader Simon Bridges yesterday said Project Speargun should be reconsidered following the 15 March mosque shootings which left 50 people dead.
The cyber-snooping proposal to scan internet traffic coming into the country was ditched by the former National government and then-prime minister John Key in 2013.
Speaking at her weekly media conference, Ms Ardern queried any "assumption" that the programme could have increased "knowledge" of the massacre ahead of time.
"That actually may not have been the case, because my understanding of Project Speargun is that it was a cyber-security initiative, rather than maybe what is being implied."
Ms Ardern said the Royal Commission into the shootings would investigate "whether or not [intelligence agencies] could or should have known more".
"New Zealand is not a surveillance state - and that's been a very clear directive, I think, from members of the public," Ms Ardern said.
"But questions of course need to be answered around whether or not these were the activities of an individual that we could or should have known."
Mr Bridges told RNZ he did not know whether Project Speargun could have prevented the terror attack, but it "would've done more to keep New Zealanders safe".
"I'm not saying it would have made the difference [in the case of the shootings]. I certainly don't think you can say it absolutely wouldn't have," he said.
"Our risk profile has changed from low to high and we should be revisiting our security settings. We should be looking at the likes of Project Speargun given the much greater ability it would have to keep New Zealanders safe."
Mr Bridges said Ms Ardern was "fudging and dodging" questions about New Zealand's surveillance laws.
"It may be a hard question for the prime minister, but actually we need and deserve as New Zealanders to understand her position on issues such as our security laws and Project Speargun."
Green MP Golriz Ghahraman cautioned the government to wait for the findings of the Royal Commission before taking any drastic action.
The public would not stand for "knee-jerk" mass surveillance suddenly being introduced, she said.
"New Zealanders have shown us over the past week that they are united in love for the Muslim community and a resolve to protect our minority communities.
"But we want to do that, as we've always done that, within a human rights framework. That's who New Zealand is. We're not America - and our reaction to this has shown that."