Thompson has proposed universal federal background checks on people who want to buy guns, including firearms sold at gun shows and online. He also wants to prohibit people on the "no-fly" list from buying guns.
Gun dealers were among those who spoke in favor of stronger rules.
"With our constitutional right to bear arms comes a responsibility to protect our loved ones, our neighbors, and anybody else from the devastating effects of gun violence," said Joe Deaser, owner of Capital Gun Club, a gun shop and shooting range in Roseville, outside Sacramento.
He said he does a background check on everybody who comes to his shop, even in instances when he's not required to by law.
"This really isn’t about gun control. It’s about keeping bad people from doing dumb things," Deaser said.
Most background checks take 90 seconds. But some take longer. And there's a loophole in the national law, that allows dealers to sell a gun if they don’t get a response in three days, said Chris Kitaeff, a gun show dealer from Phoenix, Arizona.
"What we've done, and what we urge other gun dealers to do, is to adopt the common sense code of 'no completed background check, no sale,'" he said. "Walmart, one of our nation's largest retailers of firearms, has implemented this exact policy since 2002."
But several gun advocates at the forum said they opposed measures that would make it harder for law-abiding citizens to buy guns to protect themselves. One was Chase Buchanan from a group called the Pink Pistols.
"It's a group for lesbian, gay, bisexual people who have made the decision to use firearms for self-defense against people who want to murder us. Against gay bashers, I suppose," Buchanan said.
He said discussions about gun control need to include the LGBT community.
"We're here. We're queer. We're armed. Get used to it," he said.
Sam Paredes told a story about a home intruder who went into his daughter’s bedroom. Paredes got his gun and says that frightened the intruder away.
"If I didn't have a gun, I could have lost a family member," he said.
A third gun rights advocate argued that California already has the strictest gun laws in the country, but they didn't stop the mass shooting in San Bernardino.
"Criminals, terrorists don't care about the laws," said Craig DeLuz, legislative advocate for the California Association of Federal Firearms Licensees. "Bad guys get guns no matter how strict the laws are. All these laws do is disarm law-abiding citizens."
But those who favor tougher gun laws say they're not aimed at eliminating gun violence. They're meant to reduce rates of violence, said Amanda Wilcox, legislative chair with the Brady Campaign to Prevent Gun Violence.
"When someone runs a stop sign and causes a car crash, we don't say, 'See, stop signs don't work, let's get rid of all stop signs,'" she said.
