"We don't have a definitive number on the number of Australians in Wuhan or in Hubei province because it will include a significant number of dual nationals,some of whom may not have travelled on Australian passports,they've travelled on Chinese passports for example,"the minister told 3AW on Monday.
The Chinese government also shut down other cities surrounding Wuhan,the epicentre of the coronavirus,within the Hubei province as the number of infections accelerated.
The death toll has reached 80 people in China,with more than 2700 people infected.
Wuhan mayor Zhou Xianwang told reporters late on Sunday that he expected experts would confirm about 1000 suspected infection cases being monitored,which would bring the number of patients with the virus to 3000.
Ma Xiaowei,the director of China's National Health Commission,said people carrying the virus but not showing symptoms could still infect others,with the incubation period typically about 10 days but varying from one to 14 days.
Authorities were continuing the process of contacting every person who travelled on four separate flights that brought the infected passengers to Australia.
There have been five confirmed cases of the novel coronavirus in Australia,the latest a woman who was on the last flight out of Wuhan to arrive in Sydney,and whose positive test result came through on Monday.
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The 21-year-old woman,who arrived at Sydney Airport on Thursday and later developed symptoms,is being treated at Westmead hospital.
NSW chief health officer Kerry Chant said the woman had been met at the airport by health officials and given advice on what to do if she became unwell - and had followed that guidance.
Mr Hunt said on Monday morning there had been"no sign at this stage ... of any further transmission from those initial Australian patients to anybody else who has been in contact with them".
There are no plans to suspend inbound flights from China.
Senator Payne said closing Australia's borders due to coronavirus"would be a very significant step".
Dr Chant said on Monday that anyone with symptoms of the coronavirus,which include coughing,breathing difficulties and fever,should go to their GP or emergency room.
"The main message is for people to come forward and get tested,"Ms Chant told reporters in Sydney.
"We've waived the fee for people who might be Medicare ineligible and don't have private health insurance,so there are no barriers."
Three patientsin NSW and one in Victoria had already been diagnosed with the virus,while six people tested negative in Queensland.
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Western Australia's health department said four possible coronavirus cases were being investigated on Monday afternoon,with results from three separate low-risk cases in the state having come back negative.
Victorian acting chief health officer Angela Bone said the man diagnosed with coronavirus in Melbourne had"done everything right"and that it was important people seek medical advice and take precautions.
"If you have a connection with Wuhan and you are unwell seek medical attention,"Ms Bone told the ABC on Monday.
"The really simple things that we do to protect ourselves from all infections apply here,so washing hands and cough etiquette."
With AAP,AP