Scott Morrison is itching to unlock interstate travel as new figures show border closures are costing nearly 5000 jobs a week and $84 million a day.
Australia's unemployment rose to 7.1 per cent in May as another 227,000 people lost their jobs.
The latest jobless figures are the worst since October 2001, and would be far more grim were it not for another big fall in workforce participation.
The prime minister describes the unemployment rate as heartbreaking and warns there is a long way to go as the country recovers from the coronavirus pandemic.
"This recession will be written in the stories of those who are experiencing terrible hardship," he told reporters in Canberra.
"These are our dark times, but I can see that ray of light, and I'm sure Australians can see that too, but we have to keep moving towards it and work harder each and every day."
He is open to flying in hundreds of foreign university students next month, but warned other international travellers would not be visiting any time soon.
Western Australia, Tasmania and the Northern Territory have still not announced when their border restrictions will be lifted.
Mr Morrison says they should never have been closed in the first place.
"Every state government, every territory government, federal government, local government - all of us must do everything we can to open up our economy and get Australians back into work," he said.
Two universities in the ACT want to fly in 300 foreign students next month.
South Australia has put forward a similar plan, which Mr Morrison backs but points out the state would not fully reopen until July 20.
The prime minister said there was "a bit of a glass ceiling on the economy" when it came to restrictions around overseas travel, which will be delayed until next year.
"I can't honestly see international travel more generally, people coming from all over the world to Australia again, any time soon," he said.
Meanwhile, an anti-inflammatory drug successfully used to treat coronavirus infections in the United Kingdom is likely to be used in Australia.
"It's not going to prevent you getting it, it's not going to cure it," Health Minister Greg Hunt told 2GB radio.
"But the early but high-quality evidence out of UK is that people who are very, very sick, it gives them a much better chance of survival."
The UK reported this week trials showed dexamethasone reduced death rates among the most severely ill coronavirus patients by around 35 per cent.
The widely available drug, costing about $10 over the pharmacy counter in Australia, could be used to treat the three coronavirus patients in intensive care in Australia.
Two are on ventilators.
"We know we now have an option for the doctors in intensive care to consider. There are no barriers to them using it," Mr Hunt said.
Victoria reported 18 new cases on Thursday morning, including a third Black Lives Matter rally participant to test positive.
This followed 23 new cases across Australia on Wednesday, mostly in Victoria.
Australian Associated Press