Speaking to reporters, Morrison said that despite record infection numbers, Australia's hospital system was coping with outbreaks of the Omicron variant, reports Xinhua news agency.
"You've got two choices here. You can push through or you can lock down. We're for pushing through," he said.
"The whole pandemic has been tough and Australians have shown resilience and patience and determination."
Australia on Monday reported more than 60,000 locally-acquired Covid cases for the sixth consecutive day and 20 deaths, 18 in New South Wales and two in Victoria.
Governor-General David Hurley was among the new cases. Hurley confirmed he tested positive in a statement on Sunday night.
Morrison revealed that 5,097 patients were currently hospitalised.
"There are 78 patients who are on ventilators which are well within capacity. The major stresses on the hospital system relate to workforce issues," he said.
Australia's coronavirus vaccine rollout on Monday opened up to more than 2.3 million children aged five to 11.
There were reports of general practitioners cancelling vaccination appointments for children on Monday due to a lack of supply, prompting Vaccine Taskforce Commander Lieutenant General John Frewen to call for patience.
The Australian Health Protection Principal Committee (AHPPC) on Monday endorsed a new set of national guidelines for close contacts in vital industries.
Under the new rules, close contacts of confirmed cases who work in critical supply chains, emergency services and food processing, production and distribution will be able to continue working as long as they remain asymptomatic.