South Australia has reported 3246 new COVID-19 cases, another daily record, with the spike attributed to new year celebrations.
Premier Steven Marshall said 102 people were in hospital, up from 94 on Monday, with 12 of those in intensive care.
One person is on a ventilator.
The number of positive cases across SA's prison population has also grown to 128 with the state now dealing with 16,558 active infections.
Mr Marshall said the current hospital numbers remained "well within our capacity" while the increase in cases was thought to be the flow-on from gatherings and other events on New Year's Eve.
SA's infections jumped from 2552 on Monday, but the premier said the increase was still proportionally less than in most other jurisdictions.
"We put some pretty harsh restrictions in place to make sure we didn't have a super spreader event on New Year's Eve," the premier said.
"It was a very subdued New Year's Eve, it was a very safe New Year's Eve. But we're going to continue to see our numbers track up.
"We hope to reach the peak later this month and then start coming down the other side."
Mr Marshall also revealed the arrival of 250,000 rapid antigen tests in SA, the first of 10 million the government has on order.
They will be used in hospitals and aged care settings but will not be made available to the general public.
The delivery follows a decision by a private pathology service Clinpath to close four PCR testing sites in South Australia.
The company was contacted for comment, while the premier said it had been doing an outstanding job in SA.
He said SA Pathology had the ability to fill the shortfall as it concentrated its resources on people with virus symptoms.
Almost 21,000 tests were conducted on Monday, with SA's capacity thought to be around 26,000.
Mr Marshall said some private labs were struggling to get staff and SA Health was also dealing with "critical constraints" as it coped with the immediate health needs associated with the pandemic and the problem of maintaining the necessary workforce.
"We've got to justify and juggle and balance those two objectives and try to get that balance right," he said.
The premier said with more than 80 per cent of SA's cases now the Omicron variant, the new strain was presenting the state with a "mighty challenge".
"South Australia has got through every previous wave extraordinarily well," he said.
"I know that by working together we're going to get through this wave as well."
Australian Associated Press