And as the government confirmed it wanted to introduce a mobile phone app that would help trace contacts of people who caught the coronavirus, a man was jailed for one month for repeatedly leaving hotel quarantine to visit his girlfriend.
Australia's rate of new COVID-19 infections has held at levels much lower than other countries for weeks, as the country has implemented strict social distancing rules that have closed businesses and confined people to their homes.
While insisting the tough restrictions would be maintained for some time, Morrison urged teachers to return to classrooms across the country to join "great heroes" like medical staff and supermarket workers and keep the economy ticking over.
"If you've got a job in this economy, they're essential jobs. I don't care what the job is," Morrison told 6PR radio.
"(Parents) need to keep going to work for the sake of the economy and their families. We need the schools to be able to support that."
The International Monetary Fund expects Australia's economy to contract 6.7% this year, and analysts have forecast the unemployment rate to hit double figures in coming months as the country slides towards its first recession in three decades.
To support the economy, the government has announced a A$320 billion ($205 billion) package, including $130 billion to help businesses keep staff.
Australia has reported around 6,400 cases of COVID-19, the disease caused by the new coronavirus, with the rate of daily increases in the low single digits for weeks although there have been a handful of new clusters over the past week.
The death toll rose to 63 on Wednesday after a woman in her 60s died.
Education is run by Australia's state and territory governments, and they have switched to online teaching. Most states have school holidays this week though Victorian state students have returned to online learning.
Looking to convince sceptical state leaders, health officials will present a proposal to lower the risk at schools to the national cabinet meeting on Thursday, Deputy Chief Medical Officer Nick Coatsworth said.
"It's the view of the Australian Health Protection Principal Committee that schools are safe places because of the low rates of transmission," he said, noting that only 136 of Australia's coronavirus infections were in people aged 5 to 18 years and there had not been large infection clusters in schools.
The Health Protection Principal Committee is comprised of the chief medical officer of each state and territory, and advises Australia's national cabinet.
Morrison has said Australia will need to expand coronavirus testing and increase the speed of contract tracing to limit any fresh outbreak.
The government hopes to roll-out within weeks a new app that would allow authorities see who users had been in close contact with, and to alert them if anyone nearby had contracted coronavirus.
The app would be optional, and Morrison said at least 40% of people would need to download it if it was to be useful.
The development of the app comes as Australia enforces its strict quarantine. Interstate travel is heavily restricted, and visitors have to spend 14 days in quarantine upon arrival.
On Wednesday, a man in Western Australia state became the first person to be jailed for failing to comply with the quarantine order, local media reported.