Eighty-eight Australians are feared to have contracted swine flu, with the search on for another 22 who were on the same flight as three New Zealand students now confirmed as being infected.
Federal Health Minister Nicola Roxon has called on Governor-General Quentin Bryce to ensure chief medical officer Jim Bishop can enact Australia's quarantine powers, if required, for suspected swine flu cases.
This means authorities will have the power to detain people suspected of having the potentially deadly virus.
Of the 22 Australians who were on the flight last Saturday from Mexico to New Zealand, nine are from Queensland, eight from NSW, four from Victoria and one from South Australia.
Ms Roxon says public health authorities are trying to track them down to find out if they have flu-like symptoms.
If they have, they will be asked to submit to testing and remain in isolation until the results are known.
When asked why it took three days for health authorities to begin searching, Ms Roxon said it was important to take one step at a time.
"There was a delay in the period in the students themselves exhibiting symptoms, tests needed to be undertaken," she told reporters in Canberra on Tuesday night (AEST).
"The steps were already in place while that was happening to get the records from the airlines, to then be able to get the Customs information, then to be able to inform the jurisdictions.
"We do expect ... that we would be able to get that sort of information more quickly for future instances but really that response time is quite good."
After tests at a World Health Organisation (WHO) accredited laboratory in Melbourne, NZ authorities confirmed on Tuesday three students from an Auckland high school have swine flu, with a further seven in the group assumed to have the virus.
Eighty-eight Australians are suspected of having swine flu, Ms Roxon told reporters.
Thirty-one people are being tested in Queensland, 16 in Victoria, 14 in South Australia, 10 in NSW, eight in Western Australia, five in the ACT, three in Tasmania and one in the Northern Territory.
Test results should be known in the next one to two days, Ms Roxon said.
She said authorities were not in a position to ensure people suspected of having swine flu remained in their own homes.
"Obviously we don't live in a world where we currently restrict the everyday activities of the community."
The WHO on Tuesday upgraded its pandemic threat level to four, which is two steps short of declaring a full-blown pandemic.
Professor Bishop has written to Prime Minister Kevin Rudd advising him Australia will lift its alert to the delay phase.
"We are ensuring that we are stepping up our response so that we are focused on delaying the entry of the disease into Australia and then having the ability to act to contain any outbreaks," Ms Roxon said.
She said the situation was such that it was a long way off people being forcibly detained and reports were that passengers have been cooperating voluntarily.
"There are a range of steps that would be taken well before that, increasing, for example, the presence of clinical staff, potentially having a more active screening process at our international airports," Ms Roxon said.
"We have no reason to believe that the Australian public would be anything but fully cooperative, but we do want to ensure that we have powers to act quickly when we know in a situation like this that circumstances can change very quickly."
Professor Bishop briefed cabinet on Australia's swine flu response on Tuesday.
Since midnight (AEST) on Monday, airlines servicing Australia from the Americas have been required to report any passengers with flu-like symptoms before being cleared to land at local airports.
Nurses are stationed at international airports to detect and treat anyone suspected of carrying the virus.
Ms Roxon said that as of 11am (AEST) on Tuesday, two people arriving on flights into Australia - one in Sydney and another in Brisbane - were suspected of having swine flu and have been swabbed and sent home to remain in isolation.
She said the government's current screening advice only related to flights from the Americas but that could change if there was a large number of cases identified elsewhere.
Ms Roxon said it would not be appropriate to introduce thermal scanning of passengers at airports at this stage.
New Customs forms may need to be introduced down the track that would involve people making health declarations.
The Commonwealth swine flu information hotline is 180 2007.