The potential measures come after large crowds gathered on Sydney's beaches including Bondi on Saturday, flouting social distancing advice.
Mr Morrison said the situation at Bondi Beach should be a "wake up call to take these policies seriously".
He also announced a financial package to boost the economy during the crisis.
The number of coronavirus cases in Australia has risen sharply in recent days, reaching nearly 1,100. Seven people have died.
New South Wales (NSW), home to Sydney, is the worst-affected state with 469 confirmed cases. Queensland has 221 cases and Victoria has 229.
States and territories including Victoria, New South Wales and the Australian Capital Territory have announced that they are shutting down non-essential services to try and halt the rapid spread of the virus.
The Australian Football League's 2020 season has also been suspended, with no fixtures until at least 31 May. The women's league has also been halted.
Sydney's famous Bondi Beach was temporarily closed on Saturday after crowds exceeded Australia's 500-person outdoor gathering limit. It remains closed on Sunday.
Mr Morrison mentioned the incident and appealed for Australians to show common sense when it comes to following the rules.
"You have to keep a healthy distance between each other," he said.
"If Australians can't do that on a broad scale, then they are denying the governments and the authorities the most important weapon we have to save lives and to save livelihoods, and states and territories will have to take more severe responses to deal with that."
He warned that "draconian measures" including lockdowns are set to be discussed on Sunday. He said the lockdowns could apply to areas where there have been areas of large outbreaks.
Mr Morrison also warned Australians against non-essential travel and advised that interstate holidays be cancelled.
Individual states are already imposing tighter restrictions:
South Australia, Western Australia and the Northern Territory will close their borders from Tuesday. Under the new rules, anyone arriving will be forced to self-isolate for 14 days
Tasmania, an island state, has already imposed similar travel restrictions
In the states shutting down non-essential services,
businesses including supermarkets, petrol stations and pharmacies will remain open
Schools in NSW remain open for now but school holidays meant to start on Friday in Victoria will now start on Tuesday
What was in the financial package?
Mr Morrison said the government would make available almost A$189 billion (£93 billion) to support the most vulnerable to the effects of the coronavirus crisis.
The measures include doubling income support for those on Jobseeker's allowance. Assets tests and waiting periods will be waived.
Grants of up to $100,000 will be made available for small and medium sized businesses.
Individuals affected by the coronavirus will be able to access up to $10,000 of their superannuation during 2019 and 2020. They will be able to take a further $10,000 the following year.
Australian airlines and airports will be provided with up to $715 million in support.
The financial package is the country's first stimulus package since the 2008 global financial crisis.
Mr Morrison stressed that the measures cover the next six months. "This is not a quick fix," he said. "This will not be my last visit to the podium. There will be more packages and more support."
What's happening in Asia?
Singapore has announced it will ban all short-term visitors under new coronavirus measures. Short-term visitors are also banned from transiting through Singapore. Only work pass holders who have healthcare and transport will be allowed to enter, along with their dependents.
The city state confirmed on Saturday that two people had died from Covid-19, the first virus related deaths in Singapore.
China reported 46 new cases, all but one brought in from other countries. The one domestic case was linked to a previous imported case, according to local authorities.
South Korea reported 98 new cases on Sunday. The figure suggests a downward trend in new cases. The total number of coronavirus cases in South Korea has now reached 8,897.