The City of Sydney has cancelled or postponed all non-essential events and closed gyms and aquatic centres because of the coronavirus pandemic.

Key points: An 86-year-old man died after the worst 24 hours of infections in NSW

An 86-year-old man died after the worst 24 hours of infections in NSW Health authorities say that is due, in part, to people returning from the UK, US and Europe

Health authorities say that is due, in part, to people returning from the UK, US and Europe They also said it was becoming difficult to monitor the virus' spread

As announced by the Prime Minister Scott Morrison, all public, non-essential outdoor gatherings of more than 500 people and non-essential indoor gatherings of more than 100 people have been banned.

The City of Sydney has cancelled or postponed all events of that size run by the council until further notice.

Several precautionary measures have also been introduced, including closing aquatic and fitness centres and placing restricted hours on libraries and community centres.

Gyms and aquatic centres will be closed from Friday until April 3.

"The safety of our communities, customers and staff is our top priority," Lord Mayor Clover Moore said.

The number of deaths linked to coronavirus in NSW has risen to five, and the total number of infections across the state is now at 267.

NSW Health said an 86-year-old man who had tested positive for COVID-19 died in a Sydney hospital last night.

The City of Sydney is shutting down gyms and aquatic centres. ( AAP Image: April Fonti )

A NSW Health spokesperson said: "Our condolences are with his family and friends at this time."

There have now been six coronavirus-related deaths in Australia.

NSW recorded 57 new cases since Tuesday which was the biggest spike in a 24-hour period.

During a media conference, the state's chief health officer Dr Kerry Chant said the surge in cases was partly due to the "incredibly high rates of testing in NSW".

"We have done well in excess of 25,000 tests and continue to test a large number of people each day," she said.

Dr Chant also attributed the steep rise in cases to an influx of returning travellers from a "range of countries" in recent days.

Dr Chant said the outbreak had "changed and evolved", citing high amounts of travellers from the United Kingdom, United States, and Europe.

"What we have seen is increasing cases in returning travellers from Europe and also America, adding to the previous countries that we have had ... Iran, South Korea and Hong Kong," she said.

Health authorities are scrambling to trace the people who had been in contact with COVID-19 patients to instruct those people to self-isolate and monitor for symptoms of the virus.

But Dr Chant said this was increasingly difficult as numbers continued to rise.

"We have also observed an increase in the number of cases where we haven't been able to find a source of that infection," she said.

Dr Chant said the state's limited community transmission rates is a result of NSW having "one of the most liberal testing policies" and stressed those at risk to be tested for COVID-19.

High-risk categories include anyone who has returned from overseas and developed symptoms including a fever, cough and trouble breathing, people admitted to hospital with acute respiratory infections and anyone who has come into contact with a coronavirus case.

"We have had extremely high rates of testing in New South Wales, which compares very favourably to some of the top jurisdictions testing numbers overseas," she said.

NSW Premier Gladys Berejiklian called for calm.

"I want to echo [Dr Chant's] words in that we have one of the highest number of people tested anywhere [in Australia]," Ms Berejiklian said.

Ms Berejiklian also said she supported the Prime Minister's advice to keep schools open.

It comes amid growing concern from parents that students interacting in close quarters in classrooms or congregating outside could increase infections.

"What we're urging is parents to cooperate with the key message, if you have a sick child, a child with even just something where, in the past you would have sent them to school, please act prudently and keep them home at this time," Ms Berejiklian said.

She said parents and caregivers to schoolchildren should sustain that behaviour "for a very long time, which is about six months".

Earlier Mr Morrison said he would continue to send his children to school, and cited Singapore as an example of a country which did not see accelerated rates of coronavirus infections despite keeping schools open.