Western Australia's premier has discouraged non-essential interstate travel, as a health worker who had not been overseas was confirmed among the state's four new cases of COVID-19.
WA has 35 cases of coronavirus, including one patient who remains in a stable condition in hospital.
The new cases involve three men and one woman, all aged in their 20s and 30s.
One had travelled from Austria and two from the UK, including one via Bali.
The health worker has not been overseas and it is not yet known how they contracted the virus.
The federal government has told Australians not to go overseas and urged those abroad to come home as soon as possible.
"If this doesn't work, clearly the federal government will need to close down international tourism completely and I would urge them to do that as soon as all Australians get home," WA Premier Mark McGowan said.
The state government has urged people to reconsider non-essential interstate travel and the new multi-million dollar "Do it in WA" tourism campaign launched last week has been suspended.
Regulations will be introduced to restrict visits to remote Aboriginal communities, as indigenous people are especially vulnerable to illness.
Australian Medical Association WA president Andrew Miller said WA was about 10 days behind NSW with the virus spread and encouraged more monitoring of domestic travellers.
"You can't walk in here from Taiwan, which has less than 100 cases, but you can walk in here from the east coast, which as you know has many hundreds of cases now," he told reporters.
Police are meanwhile stepping up patrols in shops amid panic buying.
"People are acting like jerks, drongos and bloody idiots ... and I'd urge them to stop," Mr McGowan said.
Ellenbrook Police posted a photograph on social media saying they were on "toilet paper patrol" at Coles "keeping our elderly citizens safe".
Mr McGowan insisted school closures were a last resort, saying it would be "catastrophic" because 30 per cent of healthcare employees would be removed from the workforce as they cared for their children at home.
"We'll also endanger grandparents who are looking after those kids."
WA Police acting assistant commissioner Craig Donaldson said a Perth officer was among the state's cases and was self-isolating at home but had no contact with colleagues.
Meanwhile, a 100-person cap on venues has forced some to close, including Connections nightclub and the Court Hotel, while Little Creatures brewery has also closed venues as a precaution so its brewers can continue operating
As of Tuesday afternoon, only people who have recently travelled from overseas or have been in contact with a confirmed COVID-19 case and experienced symptoms within 14 days are advised to be tested.
If you believe you may have contracted the virus, call your doctor, don’t visit, or contact the national Coronavirus Health Information Hotline on 1800 020 080.
If you are struggling to breathe or experiencing a medical emergency, call 000.
