SA has already tightened its border restrictions for international arrivals, lifting the quarantine requirement from seven to 14 days.

The premier has also not ruled out tighter restrictions on travellers from other states, given the presence of the variant in both NSW and the Northern Territory.

"We're learning more about the new variant every hour," Mr Marshall said on Monday.

"We'll have to take whatever action is necessary based upon medical advice, but it's still very early days with the Omicron variant.

"We now know that is in the country and what we've got to do is make sure we're as protected as possible.

"Obviously we've got to be nimble. We've got to make sure we respond to the threat as that threat morphs and changes."

In response to the Omicron variant, Australia has shut its borders to nine southern African countries, while NSW, Victoria, SA and the ACT have brought in new rules for all international arrivals.

Genomic testing has also confirmed the variant has been detected in people who recently arrived in Sydney and Darwin.

On the weekend, SA also revised testing for travellers from interstate, requiring them to have a coronavirus test within the 72 hours prior to arrival and to show proof of a negative result.

The changes came days after SA lifted most of its border restrictions, which led to a number of infections being detected in interstate arrivals.

SA reported three new cases on Saturday, no infections on Sunday and one new case on Monday.

That involved a woman in her 20s who acquired the virus while interstate.

The state's seven active infections are all in isolation but have prompted about 40 potential exposure sites, including a number of flights from Sydney and Melbourne, supermarkets, shopping centres and hotels in Adelaide and the Adelaide casino.

Mr Marshall said SA had still not recorded any community transmission of the virus since dropping most border measures.

"There is an inevitability about cases in South Australia but what we want to do is to get to those cases as early as possible," he said.

"So that we're minimising the number of people who need to have testing or potentially go into isolation."

Also on Monday, SA revised its reporting of vaccination rates to include those aged 12 to 16.

It resulted in the state's double-dosed rate falling from 80.4 per cent to 79.1 per cent.

Australian Associated Press