ALBANY, N.Y. — New York is one of seven states already banning at least some assault weapons, but Gov. Mario Cuomo has described the existing law as having “more holes than Swiss cheese.” He wants to expand the number of guns and magazines covered by the law while also making it harder for gunmakers to tweak their products to get around the ban.

Cuomo, a Democrat, will outline his proposal in his State of the State address on Wednesday, but even before he speaks, he has incited anxiety among gun owners by acknowledging in a radio interview that “confiscation could be an option” for assault weapons owned by New Yorkers.

Since the shootings in Newtown, Cuomo has been attempting to negotiate an agreement on gun laws with legislative leaders in Albany, and the talks continued into the night Tuesday, as the governor sought to reach an agreement before his speech.

According to people briefed on the talks, the governor is considering not only rewriting the state’s assault weapons ban but also proposing more expansive use of mental health records in background checks of gun buyers, lower limits on the capacity of magazines legally sold in New York, and a new requirement that gun permits be subject to periodic renewal.

New York already has some of the toughest gun laws in the country, and the debate over new restrictions here reflects a significant change in the national conversation over guns.

Cuomo, a shotgun owner, has long spoken in favor of tougher gun control but has not used his considerable political muscle to make the issue a priority over the last several years. Now, citing the recent tragedy, he is seeking to strike a deal that could be used as a model in other liberal statehouses.

“I think what the nation is saying now after Connecticut, what people in New York are saying is, ‘Do something, please,’ ” Cuomo told reporters recently. “They look to government to respond to a crisis.”

The state’s District Attorneys Association sent a letter to the governor and legislative leaders on Tuesday calling for, among other things, the elimination of a clause that allows some high-capacity magazines. And nearly 100 lawmakers have endorsed a set of proposals that includes limiting handgun purchases to one per month, requiring a new form of ballistics identification and putting in place universal background checks.

But Cuomo faces a complicated political landscape in Albany. The Assembly is controlled by Democrats who are eager for more gun restrictions, while the Senate this year is to be controlled by an unusual coalition of Republicans, who have largely resisted new gun laws, and dissident Democrats, who support more gun control.

Gun-rights advocates argue that Cuomo is wrong to focus his attention on assault weapons; of 769 homicides in New York state in 2011, only five were committed with rifles of any kind, according to the state Division of Criminal Justice Services.