Three bills have been introduced, with others to come before this month's deadline for submitting legislation.
The measures are the most stringent to date among numerous proposals introduced this year to strengthen California's firearm regulations.
Senate President Pro Tem Darrell Steinberg said he is confident Democrats can use their majorities in the Assembly and Senate to send the measures to Democratic Gov. Jerry Brown this year.
Brown has declined to comment on weapons legislation before it reaches him.
Steinberg said the measures are designed to close numerous loopholes that gun manufacturers have exploited to get around California's existing restrictions.
Those measures had been the strongest in the nation until Gov. Andrew Cuomo signed New York's new law last month.
Other proposed measures in California would ban so-called "bullet buttons" that can be used to quickly detach and reload magazines in semi-automatic rifles, and update the legal definition of shotguns to prohibit a new version that can rapidly fire shotgun shells and .45-caliber ammunition.
The state also would restrict the lending of guns to keep weapons from felons, mentally ill people and others who are prohibited from ownership.