The government has reduced outside meetings to no more than two people, as measures to limit social interactions get still tougher.
Playgrounds, outside gyms and skate parks will be closed from Monday.
Boot camps are now banned, with only two people allowed at outside exercise sessions - the trainer and the client.
The national cabinet has also strengthened advice for vulnerable groups.
Everyone aged 70 or older should now self-isolate, Mr Morrison said, describing this as "strong advice", rather than a new rule that would be enforced by fines.
The same advice to self-isolate applies to people with chronic illnesses over 60, and Indigenous people aged over 50.
"This does not mean they cannot go outside. They can go outside and be accompanied by a support person for the purposes of getting fresh air and recreation but should limit contact with others as much as possible." Mr Morrison said.
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More broadly, the entire community should stay at home, except for shopping for essentials as infrequently as possible. for medical care or compassionate reasons, to exercise, and for work and education if that could not be done remotely.
Mr Morrison said the two-person rule did not apply to a household - household groups could be larger.
States and territories would decide whether the two-person limit was enforceable in the same way most had introduced fines for the previous 10-person limit, including a $1000 fine in South Australia.
Funeral and wedding rules haven't changed, with the limit for funerals remaining at 10 people and weddings at five.
Asked why shopping centres remained open, Mr Morrison said people should be shopping as infrequently as possible, not "browsing" and not shopping for unnecessary items such as "high end fashion". But they might still need to shop for "things that they need to completely change the way they are going to live for the next six months at least", he said such as sports equipment, and games and activities for their children to use at home.
Chief Medical Officer Brendan Murphy said the new advice was "radical".
"We have to change the way we, as people, interact with each other. It is very simple. We need to all stay home unless we are going out to shop, to do personal exercise, to go to medical appointments, or to go to work or study if you can't work from home," he said.
"So anyone who doesn't need to be out of their home should be in the home. This is radical."
Professor Murphy said while there had been "a somewhat slowing of the growth in the epidemiology curve", it was not enough.
The tougher meeting rules had been recommended because authorities were not sure that existing measures would bring the slope of the curve down enough, he said.
"We have to slow it further. We have to slow it further and we have to stop the thing that's worrying us most, which is community transmission," he said. "That is of concern, particularly in Sydney and to a lesser extent in Melbourne and Southeast Queensland. There are tiny pockets of it in other states."
The criteria covering testing had been broadened in those areas in an attempt to bring transmission under control.
"It is still a precarious position. If people don't take this seriously and we get big community outbreaks they will be very hard to control," Professor Murphy said. "Every single Australian needs to take this seriously or community transmission could get out of control and we could have a situation which is as terrible as we are seeing in the US."
Mr Morrison said 1600 people arriving from overseas had been taken into quarantine in hotels on Sunday after new rules came into place at midnight on Saturday.
- For information on COVID-19, please go to the federal Health Department's website.
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- If you have serious symptoms, such as difficulty breathing, call Triple Zero (000)
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