Passengers on a Qatar Airways flight from Doha to Sydney last week are being urged see a doctor or an emergency department if they have flu-like symptoms.
A woman on flight QR908 was later confirmed as the sixth case of coronavirus in NSW.
NSW Health said the woman in her 50s flew from Iran to Sydney via Qatar on February 23. Her symptoms began within 24 hours of landing, but the woman did not visit a hospital until six days later.
In a press conference this morning NSW health minister Brad Hazzard said the government will contact the various people who had been sitting near her.
"Anyone on that flight, QR908, that arrived on February 23 at 6.50pm at Sydney Airport, should be very aware that there was someone on the flight who had the coronavirus and if they do have any of these symptoms, then, flu-like symptoms effectively, then you should get along to your doctor," he said.
"If you have any doubts or thoughts it may be the coronavirus, please ring ahead to your GP or go to the local emergency department so they are aware and can take the appropriate steps to keep everyone safe."
The warning comes amid news that hospital operating theatres will remain open over weekends and during Easter to ensure they can cope with any major outbreak of coronavirus after the first Australian died from the illness.
Australia's economy is also expected to be one of the most at risk across the globe in the face of the crisis and faces recession if China doesn't start to recover this month.
This morning, the Australian share market tumbled more than 2 per cent at the opening.
Queensland's health minister Steven Miles said they needed to ensure any outbreak, which the state's chief health officer said was likely, did not put a strain on the hospital system.
"We will be running theatres through weekends and through the regular Easter shutdown to make sure as many people get treatment as soon as possible," Miles said.
"We know that our hospitals and intensive care units will be very busy if a coronavirus outbreak occurs ... particularly around our usual peak activity in flu season in the middle of the year."
Miles also said two of the three patients repatriated off the Diamond Princess cruise ship in Yokohama, Japan, who had tested positive for coronavirus had been discharged.
However, a 78-year-old man who contracted the virus aboard the Diamond Princess cruise ship has died.
Western Australia's chief health officer Andrew Robertson on Sunday confirmed James Kwan died at Perth's Sir Charles Gairdner Hospital in the early hours of the morning.
Kwan was diagnosed with Covid-19 about 10 days ago while in isolation at Howard Springs in the Northern Territory after being quarantined aboard the cruise ship and then flown out of Japan.
Queensland's chief health officer Jeanette Young said that anyone who had been overseas in the last two weeks and "have become unwell" should immediately see their GP.
She said the state has already tested 2700 people who had returned from China and they had all been negative but warned that an outbreak was inevitable.
"I expect we will see an outbreak of the epidemic in Queensland," she told reporters on Sunday.
She added that staff at a Gold Coast beauty salon did not also need to go into quarantine after their colleague was confirmed to have coronavirus after returning from Iran.
The woman returned to Australia from Iran on February 24.
"I've got no concerns about the people who were on the plane with that lady who returned from Iran because she was thoroughly well and she only developed full symptoms at 3pm on Thursday," she said.
"I'm very, very comfortable that there is no risk for anyone on the plane she travelled back to Australia with."
This comes as the virus has spread to 33 new countries in the past nine days — bringing the total number of affected countries to more than 60.
It has wreaked havoc with the global economy and now it has been warned that Australia is one of the nation's most at-risk.
Donald Trump's former top economics adviser Kevin Hassett said he predicts the Chinese economy will contract 10 per cent in the first quarter, in annualised terms, pushing Australia's economy towards recession.
"If the coronavirus is contained relatively soon then China goes back to normal and Australia accumulates some inventories, but they send those inventories to China in April," Dr Hassett told The Australian Financial Review.
Federal Health Minister Greg Hunt said the Morrison government has a national coronavirus plan, with health authorities anticipating more cases.
"With the international spread of this virus, it is almost inevitable that we will see more cases of Covid-19 in Australia in coming weeks," he said in a statement on Sunday.
In a further effort to prevent the spread of the virus, the government announced on Saturday that foreign nationals who have been in Iran will be banned from entering Australia for 14 days.
Four new virus cases were confirmed on the weekend involving people who had return to Australia from Iran, before the ban was imposed.
NSW Health confirmed the state's fifth and six cases as a man in his 40s and a woman in her 50s who both returned to Sydney from Iran.
The two cases are not connected as they arrived on different days and on different aircraft but authorities are asking anyone on the flights to seek an immediate health assessment if they develop any flu-like symptoms. The woman flew back to Sydney via Qatar, arriving on Sunday February 23 on Qatar Airways Flight QR 908.
She developed symptoms the following day and her illness was confirmed on February 29.
The man diagnosed with Covid-19 arrived in Sydney from Iran on February 22 but did not show any symptoms until two days later and was taken to hospital. New cases in Victoria and Queensland were also people who had travelled from Iran.
A Victorian woman was confirmed as testing positive on Sunday after landing in Melbourne on Friday.
"We are particularly concerned about Iran at the moment,' Chief Medical Officer of Australia Professor Brendan Murphy said.
"It would seem to be the highest risk outside of China and cases from Iran have been exported to a number of countries." The government is also considering an update to its current travel advice for Italy, where the coronavirus has impacted Lombardy in the country's north.