Mr Duluk has been banished from the Liberal Parliamentary Party and has had his wider Liberal Party membership suspended, amid allegations he acted inappropriately at a Christmas party in December.

In a statement to parliament on Tuesday, Mr Tarzia said he had been advised police had reported Mr Duluk for assault and he did not want the independent inquiry to interfere with the ongoing police investigation.

The speaker's move comes after Mr Duluk's lawyer also asked for the independent inquiry to be halted while his client's conduct remains a police matter.

The latest development follows moves by the MP's Liberal Party sub-branch to pass a motion on Monday night supporting their local member.

The motion put the sub-branch at odds with Premier Steven Marshall who has publicly rebuked Mr Duluk for failing to come clean with him.

On Tuesday, Mr Marshall said the support for the member for Waite at the local level was not surprising.

"It's understandable. Local branches are extraordinarily loyal. They're good friends with Sam Duluk," the premier said.

But Mr Marshall said the important thing to note was the unanimous decision by the party's state executive to suspend Mr Duluk's membership.

Mr Duluk has been accused of making inappropriate comments to SA-BEST MP Connie Bonaros and slapping her on the buttocks at the Parliament House party on December 13.

There have also been allegations he made racist and homophobic comments and other conduct that has still not been made public.

Australian Associated Press