Police Minister Stuart Nash said he understood the frustration of family members who wanted their loved ones' remains returned but said recovery teams had no choice but to wait.
The first of more than 250 collections to be held nationwide was in Christchurch, where 51 Muslim worshippers were gunned down while at prayer less than four months ago.
Only one lawmaker from the 120 that sit in New Zealand's Parliament voted against the legislation in a bipartisan display of unity.
Police Minister Stuart Nash said that if lawmakers pass the bill as expected, the new law will take effect April 12, less than a month after the March 15 terror attacks.
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