Premier Steven Marshall said seven deaths were reported in the past 24 hours with checks on nursing homes revealing another six over an undisclosed period.

He said with no requirement for those deaths to be reported immediately, health officials had reached out "proactively" to ensure the data was complete.

"We don't want people to be alarmed," the premier said.

"There are deaths in South Australia, there's no doubt about it.

"What we want to do is create the fullest picture of exactly what that situation is."

SA on Wednesday reported another 2401 new virus infections, up slightly from 1869 on Tuesday, which was the lowest daily total so far this year.

Despite the rise, the figure was still down on the state's seven-day average of 2476.

Hospital admissions rose by one to 288 with 26 people in intensive care including four on ventilators.

Also on Wednesday, the state government unveiled a plan to fast track training for up to 200 newly registered pharmacists and pharmacy interns to join the state's vaccination program.

"We are leaving no stone unturned in our effort to boost the vaccination workforce and bring on additional capacity wherever possible to get South Australians vaccinated and boosted," Mr Marshall said.

"By the end of March, we know that approximately 1.2 million South Australians will be eligible for their booster dose and we're gearing up to ensure we can deliver boosters as quickly as possible."

Australian Associated Press