SA Health said on Thursday that two men in their 80s and another in his 60s were the latest virus-related deaths, taking the toll since the start of the pandemic to 172.
But it said the number of people in hospital had fallen to 142 from 192 the previous day.
Of those, 13 were in intensive care including four on ventilators.
Thursday's case numbers follow the spike to 1958 new infections on Wednesday, almost 600 more than the previous day.
The increases this week were not unexpected considering the recent return of all students to schools, the start of the Fringe arts festival and changes to work-from-home guidelines with more people returning to offices.
Premier Steven Marshall said despite the rise in cases, fewer people as a percentage were being admitted to hospital.
"So I feel extremely confident that we'll continue along that trajectory of making sure we can get back as normal a situation as possible," he told reporters.
SA's COVID-Ready Committee was due to meet on Thursday afternoon to consider changes to the state's existing virus restrictions, with some easing expected from Friday.
The remaining measures include density limits across a range of venues, a 50-person cap for family gatherings, and mask mandates for indoor public places and on public transport.
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