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ABF Commissioner Michael Outram was speaking in Canberra, days after 2700 passengers disembarked from the Ruby Princess in Sydney harbour last week, with 48 on board subsequently testing positive.
The Carnival Corp's vessel has proven to be the biggest single source of infections in Australia.
Fifty-six Kiwis were reportedly on board the ship, which arrived in Sydney on Wednesday, March 18, after a New Zealand trip that included stops in Dunedin, Akaroa and Wellington.
It arrived in Dunedin on the morning of March 12 and departed the same day, at 6pm.
Outram said on Wednesday health departments of respective states and territories were responsible for human biosecurity-related matters.
Australia's national cabinet, dubbed the 'war cabinet', will meet again on Wednesday to consider responses to the pandemic in its third meeting this week.