Democrats see an opening
But Yee told Reuters in an interview that he and other Democrats believe more can be done.
"We're looking at yearly registration, background checks of individuals who own guns. We're looking at saying to gun owners, 'You've got to keep these guns locked up when you are not using them or not cleaning them, and that you need to put trigger locks on all of these weapons,'" he said.
Democrats won a two-thirds majority in both houses of California's legislature in November, giving them even greater clout in a body that they have long dominated. Governor Jerry Brown is also a Democrat.
Yee acknowledged that some Democrats in the state legislature were "sensitive" to the National Rifle Association but said that with a Democratic supermajority, chances for more gun control legislation have improved.
The NRA said on Tuesday it wanted to contribute meaningfully to prevent another massacre like the Connecticut shootings, suggesting a sharp change in tone for the largest US gun-rights group.
Meanwhile, California Treasurer Bill Lockyer on Monday asked CalPERS and CalSTRS, the state's public pension funds, to account for their investments in gun manufacturers. Lockyer, a Democrat, proposed they divest interests in companies that make guns that are illegal under a state assault weapons ban.
Lockyer also left open the possibility of extending the move to gun sellers, as well as gun makers.
"We are not precluding the possibility of extending a divestment move to the retail sector, but right now we are focused on the source, which is the manufacturers," Lockyer spokesman Tom Dresslar said.
CalSTRS, the California State Teachers' Retirement System, said it was reviewing its investment with Cerberus Capital Management LP, following the massacre in Newtown. Cerberus owns Bushmaster Firearms International, maker of the AR-15-style semi-automatic rifle used in the Newtown shooting.
And in Washington, US Senator Dianne Feinstein, a Democrat from California, said she would introduce federal legislation this week to outlaw the high-capacity magazines and military-style assault rifles that have been used in many shooting rampages, including the one in Newtown.
Police say 20-year-old Adam Lanza killed his mother, Nancy, at her home on Friday before shooting his way into Sandy Hook Elementary School and opening fire on students and adults. He shot himself to death following the rampage, authorities say.
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