President Barack Obama is pushing a series of steps including requiring background checks on all gun sales, reinstating the ban on guns classified as assault weapons and renewing a 10-round limit on the size of ammunition magazines.
Massachusetts Gov. Deval Patrick has also proposed a series of tougher gun control measures, including limiting gun owners to purchasing no more than one gun a month and tightening access to certain types of ammunition.
Obama, Patrick and others have also said more attention needs to be paid to the role mental illness plays in gun violence.
Supporters of gun insurance say their proposal would simply require gun owner be insured and then let the market work out the details. They compare their idea to the requirement in some states that a car-owner buy insurance before being allowed to register a vehicle.
"You don't have to own a gun," Linsky said. "You don't have to drive a car."
Under the bill proposed in Massachusetts, there would be specific penalties for anyone found in possession of a gun without insurance. The fines would range from $500 to $5,000 or up to a year in jail.
Linsky said he purposely left vague the details about what level of insurance would be required or whether existing homeowner's insurance policies that cover guns in the home would suffice.
The proposal is catching the attention of gun control activists, including Boston Mayor Thomas Menino, co-chairman of the group Mayors Against Illegal Guns.
"It's a very creative idea," Menino said. "(He's) trying to put some teeth into what we are doing."
U.S. Sen. Elizabeth Warren, also called the proposal creative.
"It's time that we think about alternative ways that we can effectively deal with gun violence," the Massachusetts Democrat said. "We need better research. We need better understanding. We need to try different approaches to protect our children."
Associated Press writer Jay Lindsay contributed to this report.