A council committee will review the submissions before making a recommendation to council on whether to proceed with the reform. A vote of the council would then be needed to enact the change.
Lord Mayor Sally Capp backs the move and says it would bring the city in line with the rest of the state where e-cigarettes are included in smoking restrictions.
Other councillors expressed caution over the proposed rule at a council meeting on Tuesday night.
Deputy Lord Mayor Arron Wood said he was “not convinced” about the need for change and wanted to hear from the public.
Councillor Susan Riley said she was “on the fence” due to the contested science on the health risks of vaping.
Councillor Jackie Watts said CBD walkers were often “swamped” by e-cigarette smoke and said the amenity issues caused by vaping should be strongly considered.
Vaping advocates say there is no proof e-cigarettes pose a danger to bystanders, with Britain’s health department and the Royal College of Physicians both finding no evidence of harm from passive vaping.
Colin Mendelsohn, associate professor at the University of NSW’s School of Public Health and Community Medicine, said nicotine doses in vapers were too low to be dangerous.
“I don’t think the council really has a mandate or a responsibility to [ban vaping],” he said in March when the ban was proposed.
Quit Victoria director Dr Sarah White has said a ban was common sense and added that e-cigarettes produce an aerosol.
“The argument that there’s absolutely no emissions is not accurate,” she said in March. “We actually don’t know the long term, or even short term, health effects of … secondhand aerosol.”