Waverley College and Moriah College both confirmed with AAP on Tuesday the schools had closed after students tested positive to COVID-19.

A spokeswoman for the independent boys' school, where a year seven boy tested positive, said it implemented its evacuation plan within 90 minutes of learning about the case.

Parents were advised to immediately pick up their children while those students who couldn't be collected were driven directly home - under social distancing restrictions - on a private bus.

"The procedure this morning was incredibly calm," the Waverley College spokeswoman told AAP.

"Staff had been preparing for some time, because the school was in a hot spot."

The spokeswoman said the school, which re-opened last Monday, is undertaking deep cleaning and will advise parents about its restart date after hearing from NSW Health. The school would not open on Wednesday.

Waverley College deputy principal Patrick Brennan also told reporters the school had procedures in place to deliver schooling online in the event of an extended closure.

Moriah College closed about midday after it received confirmation from NSW Health a student, who was on campus on May 21, had tested positive for COVID-19.

The college, which started bringing students back on May 7, in a statement on Tuesday said it had activated its evacuation plan and was planning to re-open next week, with teaching to continue online until then.

"In accordance with NSW Health advice, the College has closed whilst contact tracing is conducted, and the school is cleaned and sanitised," the college said.

The evacuation comes as public school students returned to full-time classroom learning on Monday and more people headed back to on-site work.

Hundreds of security and marshalling officers were out in force across Sydney's vast public transport network to monitor social distancing and prevent overcrowding.

NSW Education Minister Sarah Mitchell said the absentee rate at NSW schools on Monday was 14 per cent - only marginally higher than the average 10 per cent rate.

"It's really a show of confidence by our parents and families in our education system ... they know that our teachers, our principals, our school support staff have worked really hard to get schools ready for children to be back," Ms Mitchell told reporters.

The NSW government, meanwhile, is urging those with even the mildest of symptoms to get tested for COVID-19 in an attempt to rapidly identify community transmission.

Two new cases of COVID-19 were recorded in the 24 hours to 8pm on Monday, both in returned overseas travellers.

Premier Gladys Berejiklian says early testing is crucial as people begin to move around the state more freely and the winter months approach.

The state government also confirmed on Tuesday premium rates for insurer iCare will be frozen from June 30 to save businesses across the NSW more than $325 million.

"The government has deferred or waived a number of taxes, fees and levies, and I have asked iCare to do the same despite the scheme being heavily impacted by market volatility associated with coronavirus," NSW Treasurer Dominic Perrottet said.

Almost 3100 cases of COVID-19 have been recorded in NSW, with more than 426,000 people tested for the virus across the state.

The state's death toll remains at 50 and one person is currently in intensive care.

Australian Associated Press