Premier Steven Marshall said 290 people were in hospital with the virus, but 47 of those were admitted for other reasons.
He said there were 29 people in intensive care with nine on ventilators, a figure later revised down to six by SA Health.
Among the 11 deaths, five occurred in aged care centres.
The new infections reported on Thursday remained below the state's seven day average of 3949 and leave SA with 35,525 active cases.
Mr Marshall said he was hopeful South Australia was "at the top of the peak" in regard to the current Omicron-fuelled outbreak.
"South Australia is in a much better position than three or four weeks ago," he said.
"I think we've very much stabilised the situation.
"Obviously, we can't be complacent ... but I'm feeling increasingly optimistic that in the coming weeks we'll be able to ease restrictions proportionally and still keep those case numbers at a point which aren't worrying our hospital system."
Also on Thursday, South Australia finally reached the 90 per cent double-dosed vaccination target for those aged 12 and over, a level initially expected in late December.
The premier confirmed South Australians who tested positive for COVID-19 would continue to quarantine for 10 days.
Suggestions the isolation requirement should be cut to five days was not something SA would sign up to, he said.
"We know that patients still have symptoms after five days, in fact after seven days," Mr Marshall told ABC radio.
"We know that from the surveys that we take. We don't want a whole pile of people who are infectious post contracting this disease out getting more people infected.
"We would just be literally lighting a fire in South Australia if we allow them to leave quarantine after five days."
The premier said a shift to a seven-day quarantine period was possible at some stage, but at the moment he believed SA had the balance right.
"We do have a more prudent approach in South Australia but I think over the longer term that's proved to be the most successful," he said.
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