"We believe it is necessary and prudent to take this reasonable step to prevent a potential tragedy," council member Lisa Montelione said in a letter her colleagues agreed on Thursday to send to Scott.
The letter describes Tampa's dilemma — it can ban squirt guns outside the convention, but not real ones carried with a concealed weapons permit — as an "extraordinary circumstance." It asks Scott to consult with the Cabinet and legislative leaders on "how best to quickly address this paramount issue of public safety."
Mayor Bob Buckhorn has said he also expects to write to Scott about the issue.
A law passed last year by the Legislature pre-empts cities and counties from passing laws regulating firearms or ammunition.
As a result, Buckhorn says Tampa finds itself facing an "absurd" irony.
"We look silly in the eyes of the world," Buckhorn said recently, adding that the city has "become fodder for the late-night comics because of something that has nothing to do with us and nothing to do with our ability to control the situation, and it's elevated by Trayvon Martin, obviously."
Legal experts have said that, with emotions running high, someone carrying a concealed weapon in the protest area could end up in a confrontation covered by Florida's "stand your ground" law, the statute at the center of the controversy over a neighborhood watch volunteer's fatal shooting of Martin, 17, in Sanford.
Buckhorn anticipates sending Scott a letter asking the state to explore a way to suspend the law temporarily during the Aug. 27-30 convention. He hopes to ban concealed weapons inside the city's proposed "Event Zone," which covers downtown and a few surrounding areas.
In the event of an emergency beyond local control, Florida law does authorize the governor to issue executive orders that carry the force of law. Among other things, the governor could "suspend or limit the sale, dispensing or transportation of alcoholic beverages, firearms, explosives and combustibles" in the emergencies.
How Scott will receive these entreaties is not clear. As of late Thursday, his press office had not responded to three Tampa Bay Times inquiries over the past week about the issue.
Despite the state law, the Secret Service plans to ban concealed weapons inside the convention. Its federal authority trumps the state law in the area that it controls to protect the Republican nominee. The agency has said no one but on-duty law enforcement officers will be allowed to take guns inside the convention's secure perimeter.