Supervisors Mark Ridley-Thomas and Zev Yaroslavsky said they wanted to direct county lawyers to study whether the county could take steps to ensure "truthful advertising" on billboards within unincorporated areas that would comply with 1st Amendment free speech guarantees.
A hearing on the issue is scheduled for Tuesday.
The Food and Drug Administration said this week it had accused the 1-800-GET-THIN marketing company of misleading advertising in its massive campaign for Lap-Band weight-loss surgery. The FDA said the company and eight affiliated surgery centers had failed to adequately warn prospective patients about risks of the surgery, which is performed under general anesthesia.
Since 2009, five patients have died following Lap-Band surgeries at clinics affiliated with 1-800-GET-THIN, according to lawsuits, autopsy reports and other public records.
An attorney who represents 1-800-GET-THIN has said the company would work with the FDA to address its concerns.