The moves come as two more Australians die from coronavirus, taking the nation's toll to 11.
Leaders in Queensland, SA and WA announced on Thursday school holidays would be brought forward, in a similar move to what Victoria and the ACT have already done.
Teachers will still be at schools so parents who have essential jobs, such as healthcare workers and people who stack supermarket shelves, can send their children.
But all other students are being asked to stay home.
Schools will return after the holidays with distance education.
Queensland Premier Annastacia Palaszczuk said heath advice that has kept schools open so far has not changed, but the pupil-free directive provides the right balance given community concerns.
NSW schools remain open but Premier Gladys Berejiklian has urged parents to keep their children at home if possible.
On Thursday, she flagged her state was readying to move into a full lockdown over the weekend, possibly ahead of Federal Government action, if the situation with the spread of the virus doesn't improve.
Victorian leader Daniel Andrews made similar comments on Wednesday.
The nation has already had two waves of business closures this week - leading to thousands of people losing their jobs - in a bid to stop people gathering in large numbers or close spaces.
Berejiklian says the success of these measures would be judged by the number of community-to-community transmissions of COVID-19, rather than total case numbers.
"I'm saying to the community that if we're not convinced we've had a sufficient amount of success, NSW will have to take further action and that's a position I've been clear on from day one," she told reporters.
"If there's a significant shift … you know you need to take further action."
But NSW chief health officer Dr Kerry Chant said the full effect of the second stage of shutdowns - in place from Thursday - wouldn't be known for some days.
The Federal Government has been tinkering with restrictions in place to slow the spread of coronavirus.
Haircuts can now be longer than 30 minutes and 10-person funeral limits can be eased in cases of hardship.
Labor says making changes some 48 hours after the restrictions were announced just adds to people's confusion.
"It's no good for the Prime Minister to blame Australians for not following the rules when the rules are so complex and confusing," health spokesman Chris Bowen told reporters.
"So, again, we renew our call for clearer, simpler and stronger restrictions, to ensure that we deal with this crisis as well and as soon as possible."
Meanwhile, visitors to Tasmania have been told bluntly to go home.
New restrictions on remote Indigenous communities are in place with all potential visitors now required to quarantine themselves for 14 days before heading in.
The Government has also broadened testing criteria, meaning more Australians can now be screened.
So far, more than 169,000 people have been tested for the disease.
Now anyone with a fever or acute respiratory infection who works in health care or aged care can be tested.
So too can people living in areas with an elevated risk of community transmission, or where there are two or more plausibly linked cases.
This takes in aged and residential care, rural and remote Aboriginal communities, detention centres, boarding schools, and military bases that have live-in accommodation.
The Australian Medical Association says the testing criteria should be even broader, so as to better understand the virus.
There are more than 2500 confirmed cases in Australia, with hundreds of people hospitalised.