They were diagnosed from 13,736 tests in the 24-hours to 8pm on Monday, compared with 10,806 tests and seven postive cases in the previous 24 hours.

Two of the new cases, from southwest Sydney, were locally acquired. The other is a returned traveller in hotel quarantine, Deputy Chief Health Officer Dr Jeremy McAnulty said on Tuesday.

One of the locally acquired case is a close contact of the funeral gatherings cluster, bringing the total cases associated with that cluster to 73.

The other local case is from a growing number with no known source, which is worrying authorities.

There have been 16 cases in the past four weeks with unidentified sources or linked to known clusters, indicating COVID-19 is circulating in the community undetected.

Among those mystery cases is a person diagnosed on Sunday who worked at Sydney Markets in Flemington while infectious on August 9, leaving scores of market-goers at risk.

Close contacts have been identified but anyone who attended the market that day between 8am and 4pm is considered a casual contact and must monitor for symptoms.

An infected person also attended Bankstown Central Shopping Centre on August 8, between 10am and 3pm, so anyone who visited the centre that day should also do so.

While the number of daily cases in NSW is decreasing, with Tuesday's numbers the lowest since July 12, Premier Gladys Berejiklian on Monday said the mystery cases left her more anxious than ever.

"That is a big concern because ... Melbourne didn't get worse because of the number of cases they had," she said.

"They had undetected community transmission which then unknowingly got to a stage where it ... formed a number of different clusters and we certainly don't want that to happen here."

Dr McAnulty says maintaining a high testing rate is crucial.

"If you have any cold or flu like symptoms at all, assume it's COVID-19 until proven otherwise," he said.

"Isolate and get tested right away."

Testing is particularly important in southwestern Sydney, western Sydney and Sydney's east.

The three new cases brings the total NSW number to 3770, after one old case was excluded after further investigation.

Meanwhile, tough new rules to stop the spread of the virus in NSW schools come into effect on Wednesday.

Formals, dances, graduation ceremonies, choirs and all social events will be banned while students must remain within their class or year groups.

Anyone with COVID-19 symptoms cannot return to school until they receive a negative test result, spectators at school events are banned and sports carnivals are restricted to local areas.

There are 122 COVID-19 cases being treated by NSW Health, with seven patients in intensive care and five ventilated.

Meantime, Victoria has also recorded its lowest daily case tally in a month, with 222 new cases reported in the past 24 hours. Sadly, 17 more people in the state have died from COVID-19 in the last 24 hours.

Tasmania's borders will remain closed until December 1.

Premier Peter Gutwein made the announcement to extend border restictions in Parliament on Tuesday, based on advice from Public Health Services.

He said the long time frame towards the possibility of relaxed border restrictions would allow the community and businesses to plan appropriately for the reopening.

"At the moment the risk posed to Tasmania by the situation in Victoria is considerable," Mr Gutwein said.

Australian Associated Press