A jump in COVID-19 cases in the state has led to more test clinics being set up including six extra sites within 24 hours.
Collectively, 54 testing clinics now operate statewide with 38 in country areas.
This includes two clinics in the Barossa Valley in response to "a number" of linked cases identified in people who live in or have travelled through the wine region's towns on Saturday, March 14.
According to SA Health, 367 South Australians have tested positive, an increase of 30 since Wednesday, March 1.
Coronavirus cases linked to travel on cruise ships have lifted from 103 to 109 in 24 hours and a rise of 74 to 78 cases is linked to the Ruby Princess.
All told, 28,828 COVID-19 laboratory tests have been performed by SA Pathology.
SA Health confirmed late on Wednesday that six patients are being treated in Intensive Care Units, five of whom are in a critical condition and one in stable condition.
All are men aged from 52 to 77 years.
SA Health stressed in an email hat "where there has been public exposure to the virus, tracing of the patient's movements is taking place".
"South Australians at high risk of exposure are being identified and contacted by SA Health with information and advice," it said.
More than 900 close contacts of confirmed cases are being contacted daily for symptom checks.
Meanwhile, Dr Tom Dodd, of SA Pathology, said in a live broadcast on Wednesday that SA was "tracking accordingly" in terms of doing the number of tests on a population basis compared with other states and territories.
He said with SA's population of about 1.8 million, about 15,000 tests per million have been performed.
"On Monday 1200 tests were done and 1500 on Tuesday," he said.
There were no concerns with rationing of testing kits.
For more updates and details, visit the SA Health website or contact the SA COVID-19 Information Line on 1800 253 787.