Scott Morrison is threatening to make a coronavirus surveillance software mandatory or keep strict social restrictions in place if not enough people sign up voluntarily.
The prime minister has also likened downloading the mobile phone tracing application to undertaking national service.
A seventh death from the virus was on Friday recorded in Tasmania, while a crew member from the Artania cruise ship died in a Perth hospital, taking Australia's death toll to 65.
More than 6500 people have contracted the disease.
A cluster of cases in Tasmania's northwest is being held up as a demonstration of how the virus can flare up at any time.
Mr Morrison says the nation needs to have a broader testing regime, better contact tracing and greater capacity to respond to local outbreaks before governments can look at easing restrictions.
The federal government is developing a contact tracing app that checks Bluetooth connections made by the phone of someone with the virus while they were contagious.
At least 40 per cent of the population would need to install it for the results to be effective.
Mr Morrison compared using the tracing app to national service.
"If you download this app you'll be helping save someone's life," he told Triple M on Friday.
He hopes some parts of the economy could be restarted in mid-May if the testing, tracing and response capacity goals are met.
But he refused to rule out making the phone tracing mandatory.
"This is the simple deal: if people download the app and more people have got it, the sooner we can start easing off on some of these restrictions," Mr Morrison said.
Labor leader Anthony Albanese - who found out about the plans in a newspaper - is concerned about the prospect of forcibly being tracked.
"One of the things that would occur if that was the government response would be people would simply stop taking their phone to places," he told reporters.
Deputy chief medical officer Paul Kelly - who has a career in field epidemiology, including contact tracing - said the app would give officials "an industrial-strength tracing ability" alongside the work already being done.
"I think we start with voluntary (downloading) and then we see how that goes," he told reporters.
In terms of relaxing restrictions, Prof Kelly said leaders would likely look to start small.
"Of course, the cafes and restaurants and so forth are an important part of our social fabric and so we'd certainly be looking closely at that," he said.
Meanwhile, there are fears the coronavirus outbreak among health workers in northwest Tasmania may have spread to three nursing homes.
A 72-year-old man died on Friday morning at the Mersey Community Hospital at Latrobe in the region.
It's been revealed a healthcare worker who tested positive for the virus did shifts at three aged care homes as well as the two hospitals in Burnie at the centre of the outbreak.
Prime Minister Scott Morrison said that worker's actions had been "very unhelpful".
"We've had someone down there not tell the truth to contact tracers about where they've been and who they've been with," he said.
"That means a lot of people have been put at risk in northwest Tasmania."
Tasmanian Premier Peter Gutwein has announced there will be roadblocks and police checks of people moving around the northwest to ensure strict rules on travel are enforced.
"We need to ensure that we contain the virus ... that we get on top of this and we shut it down," he told reporters.
Mr Morrison said the economic impact of the global financial crisis a decade ago would be nothing compared to COVID-19.
"This thing is going to hit us like a truck," he told 3AW radio.
But he's ruled out introducing a coronavirus levy to help repair the budget.
Meanwhile, the federal government has moved to underwrite critical domestic airline routes in a bid to stop the aviation industry from collapsing, but said it won't bail out Virgin Australia.
Australian Associated Press
