New South Wales’ Health Minister has asked residents to stop shaking hands with others - and instead greet people with a “pat on the back” – after confirming Australia's first person-to-person coronavirus transmissions.

Brad Hazzard confirmed on Monday afternoon three new cases of COVID-19, two of which had a "high likelihood of transmission” in the state.

One of those cases was a sister of a man who had returned from Iran with the disease, while the other was a 53-year-old male doctor who hadn't left Australia in the past three months.

The doctor had been working in a "clinical situation" and had direct contact with patients, Mr Hazzard said.

AAP

All previously diagnosed cases in Australia were people who were infected while travelling overseas.

Mr Hazzard urged Australians to be “cautious and not alarmed”, adding it would be “sensible” for people to stop shaking hands with each other.

“It’s a very Australian thing to do, put your hand out to shake hands,” he said.

“I would be suggesting that it’s time Aussies gave each other a pat on the back for the time being”

“It’s very automatic but don’t do it.”

Health authorities are also looking to contact passengers who sat near a woman with coronavirus on a plane returning to Sydney from Iran.

The woman in her 50s started to experience COVID-19 symptoms soon after she arrived back in the country on Qatar Airways Flight QR 908 on 23 February.

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Mr Hazzard said authorities were investigating the woman's exact position on the plane.

"Anybody on that flight QR 908 that arrived on the 23rd of February at 6.50pm into Sydney Airport, should be very aware that there was somebody on their flight who had the coronavirus," he said.

"If they do have any of the symptoms ... you should get along to your doctor.

There have now been 31 confirmed cases of in Australia and more than 88,000 cases globally - across 60 countries.

One Australian has died from the virus.

The global death toll from the epidemic surpassed 3,000 on Monday after dozens more died at its epicentre in China and cases soared around the world with a second fatality on US soil.

Tasmania confirms first case

Also on Monday, Tasmania confirmed its first COVID-19 case.

Premier Peter Gutwein announced a 40-year-old man who flew from Iran to Tasmania had tested positive for the virus.

"The travel was undertaken before the [Iran] travel ban was put in place on Sunday. He has had limited movement within the community and had taken all necessary precautions including self-isolation," Mr Gutwein said.

"I want to reassure Tasmanians that this case does not present as evidence of the disease spreading within the Australian or the Tasmanian community."

Director of Public Health Dr Mark Veitch said the man was "very mildly unwell but he will be managed at Launceston Hospital to provide him with clinical monitoring and support".

Additional reporting by AAP.