There are concerns thousands of people could be prevented from casting a ballot on March 19 if they are in isolation either due to contracting the virus or if they are a close contact.
On Tuesday, parliament's upper house will return to vote on a Labor opposition bill that seeks to amend electoral laws to allow anyone placed in isolation to vote by phone.
Mr Cregan has urged Premier Steven Marshall to recall the lower house on Wednesday to also vote on the bill.
"In my view, this is a matter requiring parliament's urgent attention," the speaker told the premier.
"Importantly, it is not a matter that the executive should try to resolve using emergency powers.
"I seek your agreement to recall parliament at the relevant time."
In January, Mr Cregan also called on the premier to recall parliament to deal with the growing COVID-19 outbreak following the opening of the state's borders in late November, a request quickly rejected by Mr Marshall.
At the time, SA's daily case numbers were averaging about 3800.
The seven-day average has since dropped to 1372.
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