SA reported 2389 new infections on Monday, down from more than 5000 about 10 days ago.
There were 350 people in hospital with the virus including 12 in intensive care.
The fall in new cases over recent days came as the state-backed scheme to provide free rapid antigen tests to concession card holders kicked in.
The previous federal government program to provide them free through pharmacies ended on Sunday.
Chief Public Health Officer Nicola Spurrier said testing and isolation remained critical elements of SA's virus response.
"Rapid testing allows us to find out who is infectious and along with isolation away from others and close contact management, stops chains of transmission to others," she said.
"Rapid testing also allows early access to lifesaving antiviral treatments for those more susceptible to the severe impacts of COVID-19."
Local concession card holders are allowed up to 10 tests from now until the end of September.
They will be available at more than 50 existing collection sites, which are currently used to distribute free tests to COVID-19 close contacts.
Health Minister Chris Picton said anyone eligible for the free tests was encouraged to take advantage of the program.
"As we deal with this current wave, it's as important as ever for South Australians to get tested, stay home if unwell and do what we can to reduce community transmission," he said.
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