Wind gusts of up to 140km/h are possible, especially along the west coast of Eyre Peninsula and up to 100mm of rain could fall across the Adelaide Hills.
"We remain in the middle of this event and there is a significant way to go," Premier Jay Weatherill told reporters in Adelaide on Thursday.
About 75,000 homes are still blacked out in the state's north and on the Eyre Peninsula but power is being restored to about 90 per cent of the state's properties.
Mr Weatherill warned some households, particularly in northern areas, could remain without power for at least a couple of days.
He described the storm as "catastrophic" and said it had involved weather events not seen before in SA.
Flood Watch: Susanna Parkinson with her kids Octavia - 7yrs and Banjo - 5yrs eating dinner by candle light. Photo / Keryn Stevens
"Such as twin tornadoes, which ripped through the northern parts of our state," he said.
At the height of the drama on Wednesday super cell storms with destructive winds and tornadoes ripped more than 20 transmission towers in SA's north out of the ground, bringing down three major transmission lines. Lightning also damaged energy infrastructure, with 80,000 strikes hitting the state over a short period. It caused a state-wide blackout that plunged SA into darkness.
The ongoing power supply problems have sparked calls for an independent inquiry with Senator Nick Xenophon urging the Australian Energy Market Commission to carry out a robust analysis.
The South Australian Opposition has also called for an immediate investigation.
"The situation that occurred yesterday was totally unacceptable and we need to ensure it does not happen again," Opposition Leader Steven Marshall said.
Uprooted trees are seen near a local church that was damaged following wild weather in the town of Blyth, South Australia. Photo / AAP
Federal Energy Minister Josh Frydenberg will bring the state and territory energy ministers together within weeks to discuss ways of avoiding the cascading effect of power blackouts and how to better manage the shift to renewable energy.
Mr Weatherill said the state's power system was designed to shut itself down when such heavy damage was sustained, which protected it from further damage.
He said the return of power had been efficient in such extreme circumstances, comparing it to a city-wide blackout in New York in 2003 that lasted much longer.
Emergency relief grants of $700 will be available to those without power for extended periods.
The State Emergency Service has been swamped, responding to more than 900 calls since the storms began, including many flooded homes.
"We had about 100 homes inundated across the metro area," SES chief officer Chris Beattie said.
On Thursday, a dam burst in the Barossa Valley, north of Adelaide, posing a flood risk for the town of Greenock. Mr Beattie said SA's coasts were at risk with the coming strong winds throughout the rest of the day.
"Coupled with a high tide it may indeed threaten the city defences in Port Pirie," he said.
