"The community needs to understand that it is being well handled in concert with the state and territories, and the Commonwealth government," he said.
NSW Chief Health Officer Dr Kerry Chant said that two of the three cases involved men who had returned to Australia on the 6 and 9 January.
She said the flight details for one of the cases would be forthcoming, adding that with the other two cases, the symptoms surfaced "subsequent to their arrival [in Australia]".
"For two of the cases, they became quite unwell after the flight in. And so we do not believe they're infectious at the time of their international flight.
"We are taking this in a very precautionary way. We are contacting many people [who were on board the flights] and we don't want them to be unduly alarmed. It is about early protection.
"The [three] patients are not seriously unwell. We are encouraging people to come forward and get diagnosed."
She said the health system and public health response is "robust", saying that cases have been quickly reported and tests conducted.
'No reason for alarm'
It comes after Victorian health officials confirmed Australia's first case of the deadly coronavirus.
The respiratory condition has been confirmed in a man who arrived from China last week, Victoria's Health Minister Jenny Mikakos said.
The Chinese man aged in his 50s tested positive for the virus on Saturday after visiting a GP on Thursday and going to hospital on Friday.
"There is no reason for alarm in the general community," Ms Mikakos said.
The man had been in Wuhan, the city of 11 million people and the epicentre of the outbreak, before catching a flight to Melbourne from Guangzhou on January 19.
Tests carried out in other Australian states
Meanwhile, four people in South Australia are undergoing tests as a precaution but authorities say the likelihood they actually have the condition is low.
In Queensland five people - including three from the Gold Coast - tested negative for the virus on Saturday, with four others given an all-clear earlier in the week.
Authorities are waiting for test results of one further possible case.
In Tasmania, a man in his 30s who travelled to Wuhan this month is being tested for the virus in Royal Hobart Hospital.
Travel warning raised
The Department of Foreign Affairs and Trade overnight raised the level of travel advice for Wuhan and Hubei province to "do not travel". The disease is listed as having "pandemic potential", allowing border measures to be enhanced.
Passengers arriving on all flights from China are being stopped and given health information about the virus, its symptoms and what to do if they become unwell.
Australia's Chief Medical Officer Brendan Murphy said it was important for people arriving from Wuhan - and those in close contact with them - to monitor for symptoms including fever, cough, sore throat, vomiting and difficulty breathing.
Chinese Australians cancel flights home as deadly coronavirus spreads
Experts are still learning about the virus.
"We don't know exactly how long symptoms take to show after a person has been infected but there is an incubation period and some patients will have very mild symptoms," Prof Murphy said.
China has confirmed 41 deaths from the virus, while more than 1000 people are now estimated to have been affected worldwide. Cases have been confirmed in 10 countries.
Federal and state chief medical officers held joint discussions on Saturday with health ministers expected to do the same.
Prime Minister Scott Morrison said the confirmation of a case in Australia had been anticipated and procedures are in place to manage the situation.
The infected man arrived in Melbourne on China Southern Airlines flight CZ321 from Guangzhou about 9am on January 19.
He has pneumonia and is in a stable condition, being treated in a negative pressure isolation room.
All passengers from the man's flight would be contacted as a precaution.
"He did not show any symptoms whilst he was on the flight so it's possible he wasn't contagious but there's a lot we don't know about this virus at this point," Ms Mikakos said.
The man had been staying with family and had not been out and about, which minimised the risk to the broader community, she noted.
He had also taken precautions by phoning ahead to the GP and hospital before attending and wearing a mask.
Airport screenings worldwide
Airports worldwide are screening passengers arriving from China, while Taiwan has banned anyone from Wuhan from going to the island.
Crossbench Senator Rex Patrick has called for all direct flights from China to Australia to be screened by biosecurity staff.
China has put millions of people in lockdown in an attempt to curb the virus from spreading while the 11 million residents of Wuhan have been told not to leave.
Health officials fear the transmission rate could accelerate as hundreds of millions of Chinese travel at home and abroad for the Lunar New Year, which begins on Saturday.
Scientists are beginning work on vaccination for the virus, with a team of Queensland researchers one of three teams around the world hoping to find a medication within six months.
The previously unknown virus strain is believed to have emerged late last year from illegally traded wildlife at an animal market.