ALBANY – With his members continuing to come under political fire, the State Senate’s top Republican said Monday he hopes for substantive changes to the state’s new gun-control law.

While he voted for the law, Senate co-leader Dean Skelos of Long Island said his colleagues will be pressing for changes to the bill “that are going to be more than technical.”

He cited, without elaborating, looking to keep legal in some form the present 10-bullet maximum magazine size. The new law reduces to seven the capacity of new magazines sold in New York and prohibits owners of 10-round magazines from putting more than seven bullets in them or they will be in violation of the law.

“I think we’re going to look at the size of the clips, a number of other issues, protection within your home,” Skelos said as he was walking away from a handful of reporters following a news conference on a Senate GOP tax-cut plan.

“I don’t think there’s any reason to outlaw them,” Skelos said of 10-bullet magazines already owned by New Yorkers.

“But we also have to live within the reality of what the governor feels is appropriate or not. I believe the governor is going to be pretty firm about the seven bullets, unless it’s in the home, and he’s going to be firm on the so-called assault weapons,” Skelos said.

After Gov. Andrew M. Cuomo and Skelos met on budget issues Monday evening, Cuomo repeated that he is open to “technical” corrections of the gun-control bill but said he did not consider raising the seven-bullet magazine limit to be a technical matter.

“The bill passed by an overwhelming margin. I think it’s one of the proudest acts this New York State Legislature has passed. I believe it will save lives. But again, we are open to discuss anything,” Cuomo told reporters.

The prospect for any dramatic changes, such as in the new definition of assault-style weapons to limit their sales, is all but impossible at the political level, all sides agree. But some lawmakers believe there could be changes to the law to at least allay the concerns of some gun owners. That’s a risky venture politically since many gun-rights organizations, including the National Rifle Association’s state affiliate, say they only want the law repealed without any amendments.

Skelos has come under criticism from gun-ownership groups that have major political influence over his upstate GOP colleagues, all of whom, except Buffalo Republican Mark Grisanti, voted against the gun-control bill. Skelos and all but one of his Long Island GOP colleagues voted for the package.

As for word last week from Cuomo that he wants to see an exception to the gun law for movie and TV companies to continue to shoot scenes in New York State using assault-style weapons without risk of violating the law, Skelos said, “I think the governor and the [Assembly] speaker are, but I’m not looking to protect Hollywood.”

Still, he did not rule out backing the idea for the film industry, which receives tens of millions of dollars a year in state tax breaks. Critics have said the idea sends a mixed message from politicians looking to crack down on gun-ownership statutes while at the same time letting films feature gun violence with assault weapons.

Republicans privately say fellow GOP senators who voted for the legislation are still feeling pressure from angry constituents.

Assembly Speaker Sheldon Silver, D-Manhattan, whose chamber easily approved the gun package, which includes new restrictions on assault-style weapons and ammunition tracking, said his house would listen to what Skelos might propose. “We’ll talk about it,” he said.

But he added, “I don’t see major changes happening.”

The January bill, all sides acknowledged, has numerous “technical” mistakes that critics say was the result of rushing it onto the Senate floor before lawmakers had a chance to read the provisions.

But Senate Republicans hope they can negotiate changes to the law that might relax some of the criticism coming their way as recently as last week when 5,000 or more gun-rights advocates protested at the state Capitol.

Some protestors held anti-Skelos signs, and Republicans are already worried how the issue, which will intensify as the fight moves to the courts, will affect their chances of re-election next year.

Moreover, the law has built-in effective dates that kick in over the next year, giving opponents additional opportunities to raise public concerns over the provisions.

“I’m all over my district to meet with different groups about legislation and budget issues,” said Sen. Catharine Young, an Olean Republican.

“And everywhere I go they first thank me for my no vote, and secondly, whether it’s a school board meeting or a volunteer fire dinner, they want the law changed because they feel that it penalizes unfairly law-abiding gun owners and threatens their constitutional rights.”