Three new coronavirus cases in SA

A woman diagnosed at a drive-through clinic is among three new coronavirus cases in South Australia

Three further coronavirus cases have been confirmed in South Australia, bringing the total number in the state to 12.

The latest cases are a man aged in his 60s, his partner aged in her 50s and another woman aged in her 40s, SA Health says.

The couple recently returned from Italy, while the other woman is being interviewed.

Her's was the first positive test at a newly-opened, drive-through testing facility in Adelaide.

The three news cases on Thursday followed two confirmed on Wednesday.

Of the 12 cases in SA, nine people remain in isolation in hospital while three have recovered.

Chief medical officer Nicola Spurrier said the symptoms displayed by those with recently confirmed cases were mild.

She said health authorities still considered SA to be in the "containment phase" in dealing with the pandemic.

"In South Australia, we have 12 cases and that's a relatively small number of people," Professor Spurrier told reporters on Thursday.

"We know where they are, they're going to be isolated in one of our healthcare facilities."

But she said SA might reach a stage where public gatherings could be cancelled.

"I am looking very closely at this situation," she said.

"Some of the things that we might take into account is the size of those gatherings, whether they're inside or outside and the ability of transmission to occur."