New premier Peter Malinauskas said SA Health had been asked to look at ways to ensure hospitals were could handle extra admissions in light of recently updated modelling on case numbers.
That pointed to average daily cases exceeding 8000, with possible peaks of more than 10,000, within the next few weeks.
It suggested hospitalisations could push above 250.
The modelling also showed infections and hospitalisations subsiding significantly by early to mid-May.
"What you will see in that modelling is that case numbers, even with current policy settings, are set to escalate in a rather significant way," Mr Malinauskas said.
"South Australians are entitled to know where we're at.
"People have seen case numbers go up and that looks as though it's continuing in the very near future."
SA reported another 3686 new infections on Tuesday and four deaths, with 165 people in hospital including 11 in intensive care.
Chief Public Health Officer Nicola Spurrier said the forecast increase in case numbers was being driven by the recent relaxing in some social restrictions, a lower than expected take-up for booster vaccinations, and the emergence of the Omicron sub-variant.
Latest genome sequencing on a small number of SA cases suggested 70 per cent were the sub-variant, up from 20 per cent a few weeks ago.
"It is clearly more transmissible. We're seeing increasing case numbers in other states as well," Professor Spurrier said.
"Usually, when you've got a variant and it has a biological advantage, it tends to take over."
Mr Malinauskas said a briefing with health officials had revealed SA hospitals were under extraordinary strain and had one of their worst periods last week in terms of demand.
That resulted in a move on Friday to cancel non-urgent elective surgery, a decision that was not publicly announced just a day before the state election, he said.
The premier also announced a change in the way the SA government manages the pandemic with a decision to abolish the COVID Ready Committee and put responsibility in the hands of the Emergency Management Council, a sub-committee of state cabinet.
He said the council would have more authority to make decisions.
More broadly, Mr Malinauskas expressed a desire for SA to fall into line with other states in terms of ongoing virus rules and for the state's Emergency Management Declaration to be removed no later than June 30.
He said the crown solicitor had been directed to look at other legislative options to manage the response to the pandemic, including possible reforms to the Public Health Act.
Amid concerns around the latest virus modelling, SA will keep its mask mandates and isolation measures in place but the premier said they would be key points of discussion at the first meeting of the Emergency Management Council on Friday.
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