SA Health says it is investigating a cluster of coronavirus cases among Qantas baggage handlers at the Adelaide Airport, as the state records 32 new cases.

Key points: South Australia has recorded 32 new COVID-19 cases, bringing its total to 337

South Australia has recorded 32 new COVID-19 cases, bringing its total to 337 Eight men are in ICU in SA hospitals, five of whom are in critical condition

Eight men are in ICU in SA hospitals, five of whom are in critical condition Authorities "haven't been able to ascertain" the case which infected Qantas staff yet

Six baggage handlers have tested positive to COVID-19.

Chief public health officer Nicola Spurrier said about 100 other people work in the immediate area of the airport, and a "significant number" of people would be required to self-quarantine.

Dr Spurrier recommended people who have travelled through the airport in the past 24 hours to give their bags a wipe-over.

A further 32 cases of coronavirus have been reported in SA today, taking the state's total to 337.

Late on Tuesday evening, the Department for Education announced that Renmark North Primary School, in the state's Riverland region, would be closed on Wednesday due to a staff member testing positive.

The department said via social media that public health officials were undertaking contact tracing and parents had been informed.

Dr Spurrier said three of today's cases were linked to the Ruby Princess ship, bringing the state total from that cruise to 74.

A total of 104 of South Australia's cases are from cruise ships.

Eight men, aged between 52 and 77, are in intensive care, with five of them in a critical condition.

"Today's ages range from people in their 20s to people in their 80s," Dr Spurrier said.

Authorities tracing case which infected Qantas staff

Qantas said a flight from Sydney to Adelaide on Tuesday afternoon was turned around while it was in the air because it was unable to service the aircraft.

It came after the six Qantas baggage handlers tested positive to COVID-19.

"Seven flights to and from Adelaide are affected," a Qantas spokesperson said.

"This includes one Sydney flight that was on its way to Adelaide, which will return to Sydney and passengers will be provided with accommodation and put on alternative services tomorrow."

Airline employees who might have had contact with the diagnosed staff "will be required to self-isolate for 14 days".

"We are working to minimise any disruptions to customers who are flying in and out of Adelaide, although passenger numbers are significantly reduced due to government travel restrictions," the spokesperson said.

"In addition to enhanced cleaning measures introduced since the coronavirus outbreak at airports and on aircraft, we are conducting extensive cleaning of common areas used by these employees in Adelaide."

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SA Health authorities are now in talks with Qantas about "risk mitigation".

"We haven't been able to ascertain the original case [that infected Qantas staff] at this point in time," Dr Spurrier said.

"If you have come off a flight today or in the last 24 hours it may be worth giving your bags a wipe-over and also monitoring yourself for symptoms.

"We do know that the virus can survive on hard surfaces.

"This is a serious situation and I can't provide very much more information at the moment because it's actually just been reported to me, and my staff are working through that as we speak.

"We've met with Qantas and we're looking at implementing some work-arounds to ensure that baggage can be offloaded.

"Qantas has done an amazing job bringing people home internationally and also continuing to carry people around Australia in domestic flights."

In total, South Australian authorities have carried out 27,500 COVID-19 tests, with 1,146 of those occurring on Monday.

About 900 close contacts of COVID-19 cases in South Australia are being contacted daily for symptom checks.

Yesterday the state recorded six new cases.

"It was wonderful to have smaller numbers yesterday and the day before, but obviously this is still a big issue in our community," Dr Spurrier said.

"If we need to, we will put in more measures."