Scott Morrison wants anyone who attends future anti-racism rallies arrested and charged.
The prime minister has described Black Lives Matter protests as a “real blocker” to easing coronavirus restrictions.
There have been eight new cases of coronavirus recorded overnight and one of those – a non-indigenous man in his 30s – attended last week’s rally in Melbourne.
It could be several days before authorities determine whether the “potentially infectious” man, who wore a mask to the rally, spread the disease to others.
The prime minister said the “double standard” displayed by protesters had offended many Australians.
And the potential health fallout is impeding decisions around interstate travel, funeral numbers and places of worship.
“It just puts a massive spanner in the works and that’s why it’s so frustrating,” Mr Morrison told 2GB radio on Thursday.
“They have put the whole track back to recovery at risk and certainly any further action on this front would be absolutely unacceptable.”
Deputy Chief Medical Officer Michael Kidd said the large crowds struggled to maintain social distancing.
“If we had had a person or a number of people with COVID-19 amongst those crowds, then there would have been the risk of significant transmission,” he told the ABC.
He said the result of any transmission would be seen in coming days.
The prime minister said protesters should be charged if they attend further Black Lives Matter rallies.
“It’s a free country and we have our liberty but the price of liberty is we respect our fellow Australians,” he told 3AW radio.
“Turning up to a rally this weekend would show great disrespect to your neighbours.”
Opposition Leader Anthony Albanese told people considering joining further protests to listen to the medical advice.
“Quite clearly, large public gatherings provide a risk,” he told reporters.
“They provide a risk to individuals’ health and a risk to community health.
“We need to not be complacent about coming out of this crisis. We’re not through it yet. And that’s why we need to be consistent.”
Mr Morrison has also declared JobKeeper payments will remain until the end of September for everyone except childcare workers.
“I already said that so I don’t know what that other speculation is about,” he said.
He has ramped up calls for state leaders to set a border opening timetable, with coronavirus infections at low levels.
Mr Morrison wants premiers to nominate a July date, in line with the national cabinet’s target for the third stage of eased restrictions.
Just 20 people remain in hospital with the disease, three of them in intensive care.
While 102 people have died in Australia from coronavirus, more than 6740 of the 7276 diagnosed have recovered.