Mr Marshall said he had not asked Transport Minister Stephan Knoll and Primary Industries Minister Tim Whetstone to quit, despite ongoing calls from the state opposition.

He said while mistakes should not have been made, there was ambiguity around what could be claimed under the Country Accommodation Allowance since arrangements changed in November, 2018.

"I don't think this meets the threshold. I don't think they were deliberately dishonest," Mr Marshall told reporters on Friday.

"This has been sloppy. It's unfortunate. It shouldn't have happened.

"There are rules and I expect every single member of my team and the entire parliament abide by those rules."

Under current regulations, country MPs in SA are able to claim an accommodation allowance of $234 a night for when they leave their electorates and visit Adelaide on parliamentary or other work-related business.

The allowance applies to MPs that live more than 75km from the Adelaide CBD.

On Thursday, Independent Commissioner Against Corruption Bruce Lander announced an investigation would begin into the money claimed.

Mr Marshall said the government would be fully cooperative.

Mr Whetstone has paid back about $7000 wrongly claimed while Mr Knoll has admitted to finding three errors but opted to return everything he claimed since 2018, more than $29,000.

Australian Associated Press