Victoria is getting legal advice about whether it can force returned travellers to be tested for coronavirus.
The state government confirmed on Saturday it was seeking legal advice if it could make returned travellers in hotel quarantine get tested, a day after it was revealed they don't have to in Victoria.
"It's the government's view that all returned travellers should be tested," a government spokeswoman said.
"Following yesterday's decision at National Cabinet, Victoria is getting legal advice to explore all options."
Victoria's hotel quarantine program tests travellers on arrival and the 11th day, the government said.
Victoria recorded 41 new COVID-19 cases on Saturday as the state racked up an 11th day of new cases in the double digits. That is in stark contrast to the low numbers being recorded across the rest of the country.
Treasurer Josh Frydenberg said it was important to test and trace as many people as possible to prevent the spread of the virus.
"It is very important that people do put themselves forward to have this test because ultimately if someone gets coronavirus they are endangering the lives of others across the community," he told reporters in Melbourne on Saturday.
Concerns erupted after Deputy Chief Health Officer Annaliese van Diemen revealed on Friday about 30 per cent of travellers refuse to be tested during their 14-day quarantine.
Liberal MP Trent Zimmerman said testing should be mandatory.
"Frankly, I think it is recklessly indifferent of people in quarantine not to agree to have a test, because we've seen the number of people that are in quarantine testing positive is obviously a lot higher than the rest of the population," he told ABC television on Saturday.
"If they are not prepared to do that, they shouldn't come back."
Labor frontbencher Linda Burney thought their actions were "really selfish".
"The reason that Australia is doing relatively well in terms of the virus is because of the testing regimes and we know how important they are," she told ABC television.
New testing rules in NSW quarantine
Meanwhile in NSW, returned international travellers who refuse to be tested for COVID-19 on the tenth day of hotel quarantine will be made to extend their stay by an extra 10 days.
Six new cases were reported in the state on Saturday, including a man in his 70s from Sydney's west.
All close contacts of the man, from the Penrith area, have been contacted and the case is under investigation, NSW Health said.
The remaining five new cases are returned travellers in hotel quarantine, the department said in a statement.
Less than two per cent of returned travellers in hotel quarantine have refused to take a coronavirus test on the tenth day of their stay, NSW Health said.
"NSW will ensure all returned international travellers entering Australia will either be tested for COVID-19 during their hotel quarantine at day 10, or be required to extend their quarantine by an extra 10 days," the department said in a statement on Saturday.
"NSW already requests all of these returned travellers undertake a COVID-19 test on day 10 of their quarantine, and less than two per cent have refused to take the test."
Testing on day 10 was established by NSW Health on 15 May, and since then 59 of 11,634 returned travellers have been found to be positive.
The six cases reported on Saturday bring the state's total number of coronavirus cases to 3174. A total of 58 cases are being treated by NSW Health, with none in intensive care.
A record total of 23,733 tests were notified in the reporting period, NSW Health said.
Following increased cases in Victoria, NSW has announced it will turn away football fans from the southern state.
NRL and AFL spectators trying to enter NSW stadiums from 1 July are likely to be required to show their driver's licence to prove they're not from Victoria.
Victoria continues testing blitz
Victoria has ramped up testing with its focus on 10 suburbs with high community transmission - Keilor Downs, Broadmeadows, Maidstone, Albanvale, Sunshine West, Hallam, Brunswick West, Fawkner, Reservoir and Pakenham.
Meanwhile, almost 5000 thermometers are being shipped to Victorian vacation spots as the state enters the school holidays.
Some of the 200 specialist medical and support personnel from the Australian Defence Force are understood to have arrived in Victoria to help with the state's coronavirus woes.
More than 1700 people have recovered from the virus in Victoria while 20 have died.
More cases of coronavirus are expected, with hundreds of Australians set to return from overseas in coming days to begin mandatory 14-day quarantine.
South Australia reported no new coronavirus cases on Saturday as about 260 people arrived in Adelaide from Mumbai, via Singapore. Hundreds are expected to follow from South America, Indonesia and India.

People wait in line to receive a COVID-19 test at a Coronavirus pop-up testing facility in Broadmeadows, Melbourne. Source: AAP
South Australian Health Minister Stephen Wade is preparing for about five to 10 per cent of returnees to have the virus, as was the case when people arrived from Indonesia in other states.
Despite the outbreak of coronavirus cases in parts of Melbourne, restrictions are being eased across Australia.
Prime Minister Scott Morrison says the spike in cases is being managed appropriately, and he believes it's reasonable for states to bar residents from hot spots.
"We remain on track, the curve remains flat," he told reporters in Canberra on Friday.
Except for Western Australia, all jurisdictions will restart domestic travel during July, a commitment Mr Morrison expects states to uphold.
People in Australia must stay at least 1.5 metres away from others. Check your state’s restrictions on gathering limits.
Testing for coronavirus is now widely available across Australia. If you are experiencing cold or flu symptoms, arrange a test by calling your doctor or contact the Coronavirus Health Information Hotline on 1800 020 080.
The federal government's coronavirus tracing app COVIDSafe is available for download from your phone's app store.
SBS is committed to informing Australia’s diverse communities about the latest COVID-19 developments. News and information is available in 63 languages at sbs.com.au/coronavirus