In total, there have been about 3,300 instances in which a person was charged with at least one offense established by, or strengthened under, the Safe Act, such as possessing a weapon on school grounds or buying a gun for another person who is forbidden to have one. (In those instances in which a person was charged with multiple Safe Act offenses, state records showed only the most serious charge.)

In 92 percent of cases, the charge was criminal firearm possession, a newly created felony; most of those were in either Brooklyn or the Bronx. The district attorneys in those boroughs said that in some instances in the past, those found with an unlicensed handgun could be charged only with a misdemeanor; now, they can be charged with a felony, which carries a stiffer sentence.

As he campaigns for re-election, Mr. Cuomo has trumpeted the Safe Act in some, but not all, of his appearances. At a rally in the Riverdale section of the Bronx in September, he spoke of his work on gun control, same-sex marriage and abortion rights to show how he was trying to restore New York as “the progressive capital of the nation.”

“We said, let’s take those tough issues and solve them and show leadership,” the governor said. “Let’s take the issue of gun violence, where too many innocent people have died, and let’s pass sensible gun control once and for all, and don’t tell me it can’t be done. I’ll show you it can be done. And that law is going to save lives.”

At a speech three days later in Buffalo, Mr. Cuomo discussed only same-sex marriage and abortion rights, not gun control.

In a poll conducted by Siena College in March, the Safe Act drew support from 63 percent of voters statewide. But opinions varied significantly by region: 79 percent of voters in New York City and 63 percent in the city’s suburbs approved of the laws, compared with only 45 percent in upstate New York.