"That's my plan A and I really want plan A to work."
Mr Morrison has likened using the tracing app to national service.
"I know this would be something they might not normally do at an ordinary time but this is not an ordinary time," he said.
"If you download this app you'll be helping save someone's life."
Better contact tracing is one of three main benchmarks the government wants to meet before strict restrictions can be lifted.
The other two are a broader testing regime and a greater capacity to respond to local outbreaks.
Mr Morrison says the app won't be used by police as evidence to prosecute people for breaching social distancing requirements.
Australia's deputy chief medical officer Paul Kelly says its rollout will begin on a voluntary basis.
It would allow contact tracers to have information immediately rather than waiting hours or even days as they currently do.
"The app would be an extra piece to this puzzle and that timeliness element is the crucial thing," Professor Kelly told reporters in Canberra.
Labor leader Anthony Albanese - who found out about the app in the 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.
"It's up to the government, frankly, to explain exactly what it has in mind with this app and to be very clear with the Australian public about whether it is going to be voluntary or whether it is going to be some level of compulsion involved."
Privacy issues are being worked through before an opt-in app is launched.
The app is being developed based on a Singaporean version, TraceTogether.
It uses Bluetooth to plot people who had spent 15 minutes or more in close proximity to a person with coronavirus.
They then share the records with authorities when asked to be part of a tracing investigation.
People in Australia must stay at least 1.5 metres away from others and gatherings are limited to two people unless you are with your family or household.
If you believe you may have contracted the virus, call your doctor (don’t visit) or contact the national Coronavirus Health Information Hotline on 1800 020 080. If you are struggling to breathe or experiencing a medical emergency, call 000.
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