City Council members introduced the renewed plan during a meeting on Wednesday.
The proposal would require stores with 300 or more employees to pay their personnel additional $5 an hour.
The plan comes after Long Beach passed a resolution on Tuesday that could provide grocery workers with an extra $4 an hour in hazard pay.
Stimulus update: Lawmakers close to deal that includes $600 checks, $300 in weekly jobless aid
Los Angeles County's Department of Public Health reported 138 additional coronavirus fatalities Wednesday, although seven of those had been announced Tuesday by health officials in Long Beach.
The new deaths, the highest single-day number ever reported, lifted the countywide cumulative total to 8,568. Long Beach health officials announced four additional deaths Wednesday evening, raising the overall total to 8,572.
City News Service contributed to this report.