Mr Barr said arrests were not practical and would put people at more risk by bringing them into close contact. It was better to rely on "collective goodwill and respect for the public health situation we find ourselves in", he said, describing the NSW police response to the lockdowns as "very strange" and very aggressive.

He accused Mr Morrison of double standards, after Mr Morrison said "it's a free country" when asked about anti-lockdown protests.

"This example in Victoria highlights the risks associated with large public gatherings so that should serve as a timely reminder to everyone," Mr Barr said. "But of course in a liberal democracy we do retain the right of citizens to protest. This is not Trump's America or Putin's Russia. We do not seek authoritarian responses in this country to people protesting."

In Melbourne, a protester tested positive a day after attending a rally last Saturday, prompting Janet Rice, a Greens Senator at the same event to stay away from the Senate chamber on Thursday. Four Labor MPs who attended separate protests were tested this week, all negative.

Mr Morrison said protesters who defied rules banning mass gatherings this weekend should be arrested.

"You can't have a double standard here," he said. "... People who would turn up to a rally this weekend would be showing great disrespect to their neighbours."

Mr Morrison will push hard for states to reopen their borders when the national cabinet meets on Friday, saying he is frustrated they haven't named a firm timetable.

Border restrictions are still in place in Queensland, South Australia, Western Australia and Tasmania.

"Hotels have to be provisioned. Planes have to be fuelled. They have to be ready to get back in the air and crews have to be brought back and training has to be done on COVIDSafe operating environments," Mr Morrison said. "There's a lot of work to do. So nominate the date and let's get on with it."

An OECD report on Thursday showed the Australian economy performing well compared with other countries, with its GDP predicted to fall 5 per cent this year, or 6.3 with a second wave of infections and lockdowns. That is better than any other OCED country bar Korea, and compares with New Zealand (8.9 per cent, down, or 10 per cent with a new lockdown), and Britain (11.5 per cent or 14 per cent).

Treasurer Josh Frydenberg said it was critically important that Australia maintain momentum.

"Closed borders cost jobs," he said. "There is no clear medical reason as to why domestic borders should be closed."

It is unclear whether Black Lives Matter protests will go ahead this weekend, and plans for a refugee protest in Sydney on Saturday are back in court. No protest has been confirmed for Canberra.

But Mr Morrison said last week's protests had "put the whole track back to recovery at risk" and any more protests would be "absolutely unacceptable on any terms". It would be at least a week before it was clear whether coronavirus infections had spread at the rallies, he said.

"It just puts a massive spanner in the works. And that's why it's so frustrating."

Health Minister Greg Hunt said people were protesting for 'the most noble of causes", but mass gatherings were dangerous.

"There are no safe mass gatherings, please do not go," he said.

But Greens Leader Adam Bandt said if the government didn't want people to protest it should tackle Aboriginal deaths in custody and institutionalised racism. The issue should be on the national cabinet agenda on Friday and at every national cabinet, Mr Bandt said, accusing Mr Morrison of being in denial about racism and trying to whitewash history.

Greens Senator Mehreen Faruqi accused the government of "myopic and reactionary malice". The protests were a chance to upend the system that had failed indigenous Australians, she said.

"Police brutality and systemic violence against black people is not a thing over there, it is happening right here in our own country, it's a reality that indigenous people live with every day," she said, citing the death of Aboriginal man David Dungay who also said "I can't breathe" as he died in custody in 2015.

Labor, though, urged people to follow the health advice, indigenous affairs spokeswoman Linda Burney saying there were other ways to make a point than protesting on the street.

In the Senate, One Nation Leader Pauline Hanson was blocked in an attempt on Thursday to debate a motion "that all lives matter".

The national group of chief health officers said a significant investigation was underway in Victoria to find the source of the infection and identify contacts.

The group urged people not to attend mass gatherings, saying protests were very high risk, with large numbers of people close together and difficulty finding all contacts.

Director of Epidemiology at the Doherty Institute Professor Jodie McVernon also highlighted the risks. "Seeing tens of thousands of people on the streets concerns us greatly about the potential for spread of infection, particularly because those are people who are coming together from different places, meeting together and then returning back to their usual homes and workplaces," she said.