South Australia has reported no new coronavirus cases as the state begins a six-day hard lockdown to contain a dangerous COVID-19 cluster.

The so-called Thebarton cluster remains at 23 confirmed infections with three people in hospital in a stable condition.

However, Chief Public Health Officer Nicola Spurrier said there were 17 more suspected cases.

She said as a result of contact tracing and testing, 3200 close contacts of known cases were in quarantine and thousands more were self-isolating.

Premier Steven Marshall said the statewide shutdown remained absolutely necessary to break the chains of transmission and prevent more widespread community transmission.

"The lessons of surging infections in Victoria and other parts of the world have been learnt," Mr Marshall said.

"Indecision plays into the hands of this virus.

"COVID-19 is highly infectious, extremely dangerous and very difficult to eradicate once it gets a foothold in a community.

"So we need this circuit-breaker, this breathing space for a contact tracing blitz."

Mr Marshall said SA contact tracing teams were working around the clock to track down people who may have been infected.

He also praised the thousands of South Australians who flocked to testing stations over the past two days with more than 20,000 swabs taken.

Health Minister Stephen Wade said two more testing stations would be established to cater for the extremely high demand, one in Adelaide's north and one in the western suburbs.

AAP