The jobless rate jumped from 6.3 per cent to 7.2 in four weeks, according to Australian Bureau of Statistics figures released on Thursday.

"This is the greatest economic challenge of our time, which is why the state government is responding swiftly and decisively to ensure as many businesses and jobs as possible make it through to the other side," Innovation and Skills Minister David Pisoni said.

Mr Pisoni said the government had already injected $1 billion to help preserve and create jobs, while a new website launched on Thursday would provide information to help businesses rebuild and recover.

"Small business is the backbone of the South Australian economy and is a huge employer," he said.

"That's why we will do everything in our power to support as many businesses as possible."

As part of its relief package, the government has provided $350 million for infrastructure projects, had allocated $300 million to a Business and Jobs Support Fund and had provided land and payroll tax relief.

Mr Pisoni said there had been great interest in the $10,000 emergency cash grants being offered to local businesses.

"We know that businesses in SA are continuing to do it tough at the moment, through no fault of their own," he said.

"But we're all in this together."

SA opposition leader Peter Malinauskas said while the state led on its COVID-19 health response, it was lacking economically.

His party suggested ideas to assist; including waiving state government fees, charges and taxes and council rates for impacted businesses.

"These numbers didn't have to be this bad," Mr Malinauskas said.

"The government should have delivered genuine stimulus and supported workers who lost their jobs and missed out on JobKeeper.

"It is heart-wrenching to know more than 40,000 South Australian jobs have been lost in one month."

Australian Associated Press