Two German travellers who managed to avoid quarantine after landing in Sydney, but were later caught in Melbourne, have tested negative to the coronavirus.
Federal Health Minister has ordered the Border Force commissioner to work with NSW authorities to find out what went wrong.
NSW police confirmed in a brief statement they are investigating the matter.
All passengers from Virgin flight VA838 that the Germans travelled on, and which landed in Melbourne at 1.25pm on Saturday, have been told to quarantine at home.
"Until such time as these two international travellers return their next negative test, which we remain positive about, unfortunately the 176-plus people on that plane ... are required to self-isolate," Victorian Health Minister Martin Foley said.
Mr Hunt said there are what he described as multiple layers of containment within the quarantine and border system.
"Ultimately these passengers have been picked up in those rings of containment," Mr Hunt assured Sky News' Sunday Agenda program.
"Frankly, we want to make sure every ring is impregnable so we have asked the Border Force commissioner to work with NSW on understanding the circumstances."
The scare did not prevent Victoria from further easing its mandatory face mask rules in Melbourne and other COVID-related restrictions.
Five returned overseas travellers in Sydney quarantine were diagnosed with the virus from over 9000 tests across the state, allaying fears a Sydney quarantine hotel cleaner who caught the virus at work exposed the community.
Tasmania has also joined the national quarantine effort on Sunday, with a flight from India carrying returning Australians landing in Hobart.
More than 120 passengers, including about 30 children, entered mandatory quarantine for a fortnight. It's the first of three flights scheduled to deliver overseas travellers to the island state to serve their quarantine.
Even so, Labor's foreign affairs spokeswoman Penny Wong doubts Prime Minister Scott Morrison will be able to keep his promise that all stranded Australians will be returned by Christmas.
She believes the government should have acted on the so-called Halton report that recommended setting up a national quarantine facility.
"Their failure to do that means people won't be home by Christmas," Senator Wong told ABC television's Insiders program.
On the coronavirus vaccine, Mr Hunt said Australia was still on track for a number to be available by March.
He said Australia will be monitoring the roll-out of the Pfizer vaccine in the UK and drawing lessons from that.
The vaccine will be voluntary in Australia, but Mr Hunt hopes it is taken up as widely as possible, especially by Australians in their 20s and 30s.
"This is still a dangerous, contagious and deadly disease," Mr Hunt said.
He said in the last 24 hours the world has had the highest number of COVID-19 cases in a single day, while in the last three days have been three of the four highest days of deaths.
"So this disease continues to spread around the world," he said.
"We are an island sanctuary and so what we do with vaccines, we want to make sure is about absolute safety."
