Chief Medical Officer Brendan Murphy is urging the public to practise safe social distancing due to concerns about COVID-19 cases deriving from unknown sources.
Professor Murphy said there were now 5687 cases across the country with a rise of 139 over the last 24 hours.
For about 10 per cent of these cases, the transmission of the virus is unknown, as there is no known contact with another case.
"I may sound like a broken record at times but community transmission is what worries me most of all," he told reporters in Canberra on Sunday.
"Those are the reasons we have brought in the social distancing measures and all of those measures to stop the spread."
COVID-19 has now claimed the lives of 35 Australians, including four new fatalities in NSW and one in Queensland, but a number of states have reported lower numbers of new infections.
Professor Murphy is pleading with Australians to forgo their usual Easter festivities next weekend to try to curb the spread of the coronavirus.
"We're asking you to stay with your family, in your residence, not travel where you might be unwittingly spreading the virus, not have parties where you might unwittingly be sharing the virus with people who don't have it," he said.
Meanwhile, Home Affairs Minister Peter Dutton has warned against using dodgy, imported home COVID-19 test kits, saying they pose a risk to public health.
A number of these kits from China and Hong Kong have been intercepted by Australian Border Force officers in the past few weeks.
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