South Australia has a new case of COVID-19 as the state enters its first full day of lockdown and the list of potential exposure sites linked to a new cluster of cases continues to grow.

SA Police Commissioner Grant Stevens said on Wednesday the case was a person who went to the Burnside Village shopping centre in Adelaide’s east.

This brings the total number of positive cases to six. The new case will be included in data to be announced by the Health Department later on Wednesday.

More than 35 sites have been listed across metropolitan Adelaide with more likely in the coming days and there are signs the virus could have spread south.

“We are now talking about the wider metropolitan area,” Mr Stevens told ABC radio.

• See all of SA’s latest exposure sites here

The outbreak is linked to an 81-year-old man who recently arrived in Australia from Argentina and quarantined in Sydney before travelling to Adelaide where he tested positive.

During the week-long lockdown, South Australians can leave home only for five reasons – to provide essential care, to seek medical assistance, to buy essential food and other goods, for essential work, or to exercise for up to 2.5 hours.

They must also wear masks when outside their homes.

Schools have closed, along with most shops. All construction work has ceased.

Premier Steven Marshall said it was vital for SA to “go hard and go early” to have any chance of containing the outbreak now confirmed to involved the Delta variant of the disease.

“We hate putting these restrictions in place but we have one chance to get this right,” he said.

“We are moving as quickly as we can to slow and stop the spread of this cluster.”

The lockdown has prompted a federal government declaration of a coronavirus hotspot for metropolitan Adelaide, the Adelaide Hills and for Gawler, north of the city.

That will trigger payments of up to $600 a week for people who lose more than 20 hours of work.

The outbreak has already plunged thousands of people into quarantine, with more expected to be forced into 14 days of isolation.

Chief public health officer Nicola Spurrier urged everyone, especially those in quarantine, to stay home.

“The virus doesn’t have legs, it moves around when people move around,” she said.

“If people stay put we will be able to get on top of it.”

-AAP