SA premier signals 'new phase' of coronavirus outbreak as new cases slow down

South Australia Premier Steven Marshall says caution is still needed but that the growth of coronavirus cases around Australia is slowing.

"We are moving into a phase now, where the numbers are not moving in an exponential growth rate," Mr Marshall said.

But he warned that the state had been home now to three "very significant" clusters of the virus - from cruise ships, in the Barossa, and at Adelaide Airport.

South Australia has had a "relatively low" 11 new cases overnight, bringing the state total to 396.

State Chief Health Officer Dr Nicola Spurrier said three of the new cases had come from the Ruby Princess cruise ship, bringing the total to 84.

All of the new cases were found in adults, with victims aged from 20 to 60.

So far, 18 people are being treated in hospitals, with eight aged 52-74 in intensive care units.

Border control measures are still in place, with police having checked about 9500 people entering the state to date.

About half have been ordered to self-quarantine, with the other half found to be essential travellers.

Mr Marshall said despite the optimistic news about the low growth in new cases, it was "no time for complacency" and people needed to continue to follow social distancing and self-isolation orders.

"This is a very, very nasty virus," he said.