Four more deaths have also been confirmed with 219 people in hospital with the virus, including 18 in intensive care, five on ventilators.
The state's active infections stand at 13,292.
SA's new cases on Tuesday represented a slight increase on the 1027 reported on Monday.
Chief Public Health Officer Nicola Spurrier said it was pleasing new infections remained "on the lower side" though increasing numbers of children were testing positive after the return to school.
"This is not unexpected, but things are going in the right direction," she said.
Education officials confirmed reception classes at four primary schools had been shut down and students sent home for the rest of this week after multiple virus infections.
One of those schools, Craigburn Primary, said the decision was taken after a risk assessment by SA Health when a number of cases emerged in two reception classes.
It said the closure would act as a "circuit breaker".
"Thank you to the families who have informed us early of their child's positive case," Principal Paul Luke said in an online post.
"This has helped us to identify classroom contacts and send out communications to the affected families."
SA students in reception and years 1, 7, 8 and 12 have been back in classrooms for two weeks while other years returned on Monday after two weeks of online learning.
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