The government has reduced gatherings to no more than two people unless they are direct family or household members, as measures to limit social interactions get still tougher.
Prime Minister Scott Morrison also announced that the states and territories will impose a moratorium on evictions for commercial and residential tenants for the next six months.
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.
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 gathering 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.
ACT Chief Minister Andrew Barr said ACT authorities would warn people in the first instance but were moving to impose stronger measures such as fines to ensure consistency across the country. The fine level would be worked out in the next 24 hours, he said on Monday morning, and would be consistent with NSW.
Mr Barr said the government would also develop more support for elderly Canberrans to allow them to remain at home.
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.
The "curve" is the rate of increase, which in Australia has been climbing at more than 20 per cent a day for more than two weeks. But since Wednesday (March 25), the rate has slowed, with daily increases of 16 per cent or less. The increase in case numbers from Saturday to Sunday was 9 per cent. An extra 331 people were diagnosed, for a total of 3966.
"It is still a precarious position," 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."
The government has progressively shutdown gatherings, closing restaurants, cafes, pubs, nightclubs, theatres and other venues last Monday - other than takeaway. Then from Wednesday March 25, food courts, open homes, beauty salons, galleries and churches were closed, without outdoor restrictions limited to 10 people. Less than a week later, that is down to two people and the limit applies to any public space, including shopping centres. Shops and schools remain open, although a number of shops have closed their doors and most schools are asking children to stay home if they can.
On the eviction moratorium for tenants, Mr Morrison said there was still work to be done, but the governments would develop measures to encourage tenants and landlords to come to an agreement.
"If you aren't going to engage in that sort of cooperative activity, between bank, between tenants and between landlords, then the sort of support that you might otherwise expect to receive, you will not receive," he said.
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.
Medicare-subsidised telephone consultations begin on Monday, and Mr Morrison announced $150 million for domestic violence support, with a 75 per cent increase in Google searches related to domestic violence.
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