Tense wait for more than 100 health workers who were forced into isolation after coronavirus clusters emerged at two hospitals

Health authorities are working to stem the impacts of a coronavirus cluster emerging at two Sydney public hospitals, with more than a hundred workers in isolation waiting on test results.

There were four new COVID-19 cases in NSW on Monday - a returned overseas traveller and three healthcare workers at Sydney's Concord Repatriation General Hospital and Liverpool Hospital.

The three healthcare workers were diagnosed during investigations into an emergency department doctor, reported on Saturday, who worked at the two hospitals while infectious.

Another case, a visitor to a hospital emergency department where the doctor worked or sought treatment, will be included in Tuesday's numbers, taking the cluster to five.

Patients considered close contacts and all staff at Concord and Liverpool EDs at the same times as the positive cases are being isolated and tested.

The three newly reported health workers say they had no symptoms while at work, and also wore personal protective equipment while caring for patients.

Chief Health Officer Kerry Chant said there was no evidence to suggest NSW hospitals weren't operating safely and effectively, and urged people not to delay urgent care.

Authorities suspect at least one of the new cases caught the virus while both parties were wearing masks.

'For some of the cases there isn't that clear-cut direct contact without a surgical mask,' Dr Chant told reporters on Monday.

'We are exploring avenues of whether there could be fomite transmission.

'What that means in lay terms is if your hands are contaminated, and then you're touching computer screens or touching pens and pencils pieces of paper, can you actually transmit the virus?'

Meanwhile, Premier Gladys Berejiklian on Monday confirmed school formals and graduations would be allowed to go ahead in term 4, Despite a number of outbreaks in schools in recent months.