The number of global coronavirus infections has exceeded nine million.
Mr Hunt appeared to suggest international borders would be shut until a vaccine was found.
Australia's top medical adviser on the coronavirus pandemic says there's a "lot of luck" involved in the caseload when comparing Victoria and NSW.
Victoria's active cases have more than doubled in a week, with 16 new infections on Monday taking the total to 125.
By contrast, active cases in NSW have jumped by 22 in the past week, but fallen or remained at zero in every other state.
Victoria's case numbers are now the highest they've been in more than two months after six days of double-digit growth.
The spike caused the West Australian government to shelve a plan to open its borders in August and sparked a warning by NSW against visiting Melbourne.
Asked about the figures, Chief Medical Officer Brendan Murphy told reporters on Monday: "I think there is a lot of luck in this."
He said NSW had been better at bringing community transmission under control by using measures such as pop-up clinics in hotspots.
But he said he did not see any reason why Victoria's cases should force other states to change their plans.
South Australia will send a team of experts to Victoria on Tuesday to help with contact tracing, spending three weeks helping health officials.
WA Premier Mark McGowan has declined to put a date on when the state's borders will reopen, but internal coronavirus restrictions will be removed by July 18.
Meanwhile, the first results from the clinical trials of several different candidate vaccines should be known by late July.
Professor Murphy said the government was examining Australia's capacity to manufacture vaccines if a working one is found.
Volunteers are being recruited for a possible COVID-19 vaccine trial in Adelaide.
Researchers at the Royal Adelaide Hospital are looking for about 100 healthy adults for the trial which may be conducted later this year.
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.