The regulation of guns has been a major subject of debate in Albany in the wake of the Newtown shootings. In January, Gov. Andrew M. Cuomo, a Democrat, pushed a package of new gun laws through the Legislature, including an expanded ban on assault weapons and high-capacity magazines, as well as a requirement that background checks be conducted for private sales that do not take place at gun shows.

And some lawmakers would go further. State Assemblywoman Linda B. Rosenthal, a Manhattan Democrat, introduced a bill on Thursday that would prohibit children younger than 12 from attending gun shows. “Children should be learning to read and write, not to shoot a firearm,” she said.

The shows have long been a major area of concern for gun-control advocates. Many states either do not regulate them or have only modest rules for them; New York is among a small number of states that require background checks for private sales at shows.

Dr. Garen J. Wintemute, the director of the Violence Prevention Research Program at the University of California, Davis, described New York’s new measures as a good step.

“It’s clear that undocumented private-party sales are an important way for either prohibited persons or those who are getting guns with criminal intent to get those guns,” Dr. Wintemute said. “The majority of them probably occur elsewhere — many of them these days occur on the Internet — but you do what you can do.”

Under the state procedures, participating gun show operators are to track the firearms that go in and out of their events. Most shows will use a system in which guns brought by private sellers are tagged at the show’s entrance with the name of the owner or seller and the gun’s serial number.

When someone buys a gun from a private seller at the show and passes a background check conducted there by a federally licensed firearms dealer, a second tag will be affixed to the gun to indicate the screening was done. When guns are taken out of the show, they will be checked to ensure that the gun either is leaving with the owner or seller who brought it in, or has the second tag.