Confirmed cases rose by 198 over the 24-hour period to Saturday afternoon, bringing the national total to 5,548, health ministry data showed. The death toll from COVID-19, the respiratory disease caused by the virus, rose to 30.
That kept the country's daily new infection rate at about 5%, significantly below the 25-30% increases recorded around two weeks ago, but officials stressed it was still too early to claim victory.
"What I really would caution against is thinking we have got through this completely, because we definitely have not," Deputy Chief Health Officer Paul Kelly said in a televised briefing. "We really have to be hypervigilant now."
Australia has imposed strict social distancing, including limiting public gatherings to just two people. State borders, cafes, clubs, parks and gyms have been closed. Several states have also given police the power to enforce the rules via hefty on-the-spot fines and potential jail terms.
"All of the hard work of Australians is beginning to yield real dividends in terms of lives saved and infections prevented," Health Minister Greg Hunt told Sky News. "Every one of us can save a life, or any one of us, by doing the wrong thing, could risk a life."
In Sydney, New South Wales (NSW) state police were coordinating the movements of five foreign flagged cruise ships, carrying hundreds of crew, as they entered the harbour to refuel and stock up on supplies before returning to their home ports.
Cruise ships have become a flashpoint in Australia's response to the pandemic, with public anger after Carnival Corp's Ruby Princess was last month allowed to disembark passengers in Sydney, many of whom later tested positive for COVID-19.
Cruise ships are responsible for around 20% of Australia's coronavirus cases. Seven deaths and more than 600 infections have been attributed to the Ruby Princess alone.
Australia's decision to close its ports has led to tense negotiations with several ships still in its territorial waters.
The operation in Sydney Harbour on Saturday was also allowing crew transfers among ships to enable workers to join the vessel heading closest to their home.
While cruise ships were being ordered away, the foreign ministry said on Saturday that workers from Pacific countries who are employed as fruitpickers and farm workers would be allowed to extend their visas for another 12 months.
"This will enable them to support themselves and continue to make a critical contribution to Australia’s agriculture sector and food security," Foreign Affairs Minister Marise Payne said in a statement, noting that many were trapped in Australia because of the country's ban on international travel.
Several Australian research bodies have joined the international hunt for a COVID-19 vaccine or treatment against the virus.
The Commonwealth Scientific and Industrial Research Organisation (CSIRO), Australia's top biosecurity research agency, said on Saturday it has received A$220 million ($132 million) from the government to update its facilities.
On Thursday, Australia's national science agency, which is operated by CSIRO, said it had commenced pre-clinical testing of two potential vaccines at its high-containment biosecurity facility near Melbourne.
Meanwhile, Monash University in Melbourne said a study it is leading has indicated that a widely available anti-parasitic drug Ivermectin, used for treating lice, can kill the coronavirus growing in cell culture within 48 hours. Trials, however, needed to be carried out in people and authorities warned people against self-medicating.
In neighbouring New Zealand, the number of confirmed cases rose on Saturday by 52 to 824, according to the health ministry data. New Zealand has reported one death so far from COVID-19.