SA Health reported 13 deaths on Thursday, ranging from a man in his 50s to two women in their 90s, the result of reconciled notifications over the past two weeks.
They came as the state also recorded another 1953 COVID-19 infections, below the seven-day average of 2215.
Premier Steven Marshall said 288 people were in hospital including 27 in intensive care, where five people remained on ventilators.
With active cases dropping to 25,735, the premier said it appeared South Australia had gone past the peak in the current Omicron outbreak.
"Things are tracking well at the moment, but we can't be complacent," he said.
The new infections came as SA relaxed its work-from-home advice, allowing offices to bring back up to 25 per cent of their staff.
The premier said while the change was not as big as some people would like, it was a good first step to help revitalise Adelaide's CBD.
"Our primary responsibility is for the safety of all South Australians," he said.
"We'll monitor what happens with this but naturally we do want to increase the number of people going into the CBD.
"But we want to do it in a safe way."
Under the changes, workers are urged to wear masks even while indoors and to take lunch breaks outside.
The work from home advice was introduced in late December amid a surge in coronavirus infections.
At the same time, SA also imposed tougher density rules for most venues, including all hospitality businesses, and a 10-person cap on family gatherings.
Those measures remain in place with the premier indicating the density restrictions were likely to be the first to be relaxed.
It remained unclear if SA's public school teachers would strike on the first day of term next week after the Australian Education Union put a series of demands to the government, including the wider use of rapid antigen tests.
Mr Marshall said while the government still believed there was no need for the strike on February 2, it remained at odds with the union on the issue of RATs.
"The use of rapid antigen tests, not applied correctly, could give a false sense of security to teachers," he said.
"It's highly inaccurate in terms of giving false negatives."
However, the Health Services Union said the Women's and Children's Hospital in Adelaide had reversed its stand on the tests and would now supply the kits to frontline staff.
"We are very pleased with this outcome, this is an additional layer of protection for both the staff and the patients they care for," branch secretary Billy Elrick said.
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