CANBERRA - South Australians have been urged to "stay calm" as state authorities undertake a large coronavirus tracing operation.

More than 1,100 South Australians have been ordered to self-isolate as the state tries to prevent a cluster of COVID-19 cases linked to a school from becoming a full second wave of infections.

Seventy adult students at the school have been put into isolation for 14 days under police guard while another 1,100 students and staff considered "casual contacts" have been ordered to self-isolate at home to stop the potential spread of COVID-19.

It comes after two adult students who attended classes at the school earlier in the week tested positive for the virus.

Nicola Spurrier, South Australia's chief public health officer, said the measures were taken as a "precaution," imploring those affected to "relax, stay calm, and enjoy a little bit of a break."

"We are not leaving any stone unturned ... because as people know we have really enjoyed a fantastic lifestyle here in SA with our lifting of restrictions," she told Adelaide's FIVEaa radio on Friday.

"Even just one case in the wrong place can get out of control very quickly.

"This is safest, not only for the young people who may develop symptoms, it means we can monitor them very closely every day, but also for their families as well."

With Victoria experiencing a second wave of infections significantly bigger than its initial wave authorities in the seven other states and territories have slowed the rate at which they are easing coronavirus restrictions over fears of outbreaks.

"The entire country is on high alert and Victoria is still not at its peak," Steven Marshall, premier of South Australia, said.

As of Thursday there have been 457 confirmed cases of COVID-19 in South Australia.