Liccardo proposed the "harm reduction" measure to the City Council on Monday asking gun owners in the city to either buy the insurance or make payment to compensate "taxpayers for the public costs of firearm violence in America's 10th largest city", Xinhua reported.
The mayor's proposal came a few weeks after a mass shooting that killed three people, including two children, at an annual garlic festival in Gilroy city south of Silicon Valley on July 28.
Liccardo said his idea stemmed from California vehicle laws that would punish any misdemeanour of operating a vehicle without insurance.
"We require motorists to carry automobile insurance, and the insurance industry appropriately encourages and rewards safe driver behaviour," he said.
He admitted that the proposed ordinance is far from a complete solution to gun-related violence, but it would help reduce the harms of firearms, without waiting for Congress to take action.
"Mayors don't have the luxury of just offering 'thoughts and prayers' while gun violence tears communities like mine apart. Without congressional action, we can't end gun violence but we're going to stop paying for it," Liccardo tweeted on Monday.
The US House of Representatives has passed two bills on tightening up background checks for people who intend to buy guns, but the bills have stalled in the Senate, which will not convene until September.
Liccardo's proposal will have to be approved by the City Council, and if it becomes a law, it would make San Jose the first US city to adopt such a stern gun-curbing measure.
( With inputs from IANS )