Premier Steven Marshall said testing numbers on Saturday were "a new record", with 23,719 swabs received.

"It is very clear to me that South Australians are taking this lockdown order very very seriously," he said on Sunday.

"We want to come out on Tuesday and the actions of all South Australians are speaking volumes. Thank you very much."

Chief Public Health Officer Nicola Spurrier said one of the cases was a returned traveller, a young child of a parent who had already tested positive.

There were two cases associated with the Modbury Hospital cluster, bringing the number of infections linked to that cluster to 18.

One is a woman in her 40s and the other is a man in his 70s.

"He was quarantining at home, he lives alone and so when we got the result through he was contacted and he has now been transferred to (the Tom's Court medi-hospital)," Professor Spurrier said.

The cluster in SA began with an 81-year-old man who recently arrived in Australia from Argentina and was quarantined in Sydney before travelling to Adelaide, where he tested positive.

Genomic testing has confirmed the man became infected while in Sydney, not while in Argentina.

One new testing centre opened on Saturday and another, to be run by the defence force, is close to operational.

Bad weather on Saturday morning forced the temporary closure of the Adelaide's largest centre, the Victoria Park 24-hour site.

Mr Marshall said on Sunday this centre was still not operational.

Australian Associated Press