No clear link has emerged between the Connecticut rampage and the gunman Adam Lanza’s interest in video games. Even so, the industry’s detractors want to see a federal study on the impact of violent gaming, as well as cigarette-style warning labels and other measures to curb the games’ graphic imagery.

“Connecticut has changed things,” Representative Frank R. Wolf, a Virginia Republican and a frequent critic of what he terms the shocking violence of games, said in an interview. “I don’t know what we’re going to do, but we’re going to do something.”

Gun laws have been the Obama administration’s central focus in considering responses to the shootings. But a violent media culture is being scrutinized, too, alongside mental health laws and policies.

“The stool has three legs, and this is one of them,” Mr. Wolf said of violent video games.