The latest figures show ambulances were ramped outside hospitals for a total of 3838 hours in June, a 12.5 per cent increase on the previous high of 3412 hours the previous month.
Ramping hours had fallen to less than half of those figures in February before rising in March.
On Friday, SA Health's dashboard showed ambulances were spending an average of 109 minutes at Flinders Medical Centre before being cleared, while at Royal Adelaide Hospital the figure was 64 minutes.
The shortest clearance time was 28 minutes at the Women's and Children's Hospital.
The state's newly elected Labor government campaigned on a promise to bring ramping under control and Health Minister Chris Picton said the latest figures were "clearly unacceptable".
"We don't have enough capacity in the system. We've committed over 550 beds in addition to what we have at the moment but these will take years to build, unfortunately," he said.
"We have opened up every single bed in the health system at the moment. We're using every possible hospital site that we can at the moment."
Mr Picton said additional beds had also been secured across the private hospital network.
The current situation was being exacerbated by delays in patients being discharged, the minister said.
This week there were 250 NDIS clients in hospitals, including 120 who were ready to be discharged but had no appropriate place to go.
There had also been a recent rise in COVID-19 related admissions and influenza cases, a factor expected to continue in the weeks ahead.
Recently modelling suggested daily coronavirus infections could peak around 6000 by mid-July amid a new wave of Omicron cases.
Mr Picton said there was no doubt the hospital system was under huge pressure and the situation was "very serious".
"We are in a situation where we are seeing delays in people getting the care that they need," he said.
"But we are working day and night to try to find additional capacity."
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