South Australia has reported a fourth case of COVID-19 as the state begins a round of tough new restrictions and authorities race to contain an outbreak of infections amid a growing list of exposure sites.

The cases include an 81-year-old man who entered the country from Argentina, his daughter and another two men.

The fourth case, revealed on Tuesday, is a man who is a close contact of the elderly man and was already in quarantine.

The outbreak has plunged thousands of people into quarantine with the list of more than a dozen exposure sites including at least four major shopping centres in Adelaide’s north and northeastern suburbs.

Premier Steven Marshall said the situation was of great concern.

“We only have one chance to get this right. Our focus from day one has been to go hard and to go early to minimise the level of disruption,” he said on Monday.

“We’ve got to respond quickly.”

Tweet from @SAHealth

Late on Monday, multiple new exposure sites linked to a person with COVID-19 were revealed, including a Coles supermarket at the Greenacres Shopping Centre in Adelaide’s north-east and a number of shops and a TAB at Munno Para in the north.

New restrictions in SA include a density change to one person to every four square metres in all venues, while team and contact sport has been cancelled.

All dining must be seated, and there is a ban on dancing and singing.

Masks are required in all indoor public areas, including shopping centres, and also on public transport and in high-risk settings.

Fitness centres are closed, along with other non-essential retail.

Supermarkets and pharmacies and other essential businesses will continue to trade.

Family gatherings, including weddings and funerals, are restricted to 10 people but schools have remained open.

The new rules will be reviewed on Friday.

Police Commissioner Grant Stevens said while SA was not moving to a full lockdown, the restrictions were significant.

“We know there are people who will struggle as a result of these changes. But the consequences of not taking action could be even more severe,” he said.

“The intent here is to dramatically suppress all discretionary activity in the community.”

Authorities said earlier that the elderly man had returned to Australia through NSW, where he spent 14 days in quarantine.

He returned to SA on July 8 and presented to a suburban hospital over the weekend after developing symptoms.

The man has been admitted to hospital. Adelaide’s other positive cases have been transferred to the Tom’s Court Hotel, which is used to quarantine all those with an active infection.

“We don’t draw any conclusions as to where this infection came from. We simply don’t know and it is very early days,” Mr Marshall said.

“Our primary concern at the moment is putting everyone who may have come into contact with this person into quarantine as soon as possible.”

Business SA chief executive Martin Haese said new restrictions were another blow to the already struggling hospitality, events, tourism and retail sectors.

“We are concerned by this sudden turn of events and recognise South Australia is in a precarious health situation,” he said.

“We hope there will be no extension to the restrictions beyond Friday.”

-AAP