“The violence in the entertainment culture — particularly, with the extraordinary realism to video games, movies now, et cetera — does cause vulnerable young men to be more violent,” Sen. Joe Lieberman, I-Conn., said.

“There might well be some direct connection between people who have some mental instability and when they go over the edge — they transport themselves, they become part of one of those video games,” said Gov. John Hickenlooper of Colorado, where 12 people were killed in a movie theater shooting in July.

White House adviser David Axelrod tweeted, “But shouldn’t we also quit marketing murder as a game?”

And Donald Trump weighed in, tweeting, “Video game violence & glorification must be stopped — it is creating monsters!”

There have been unconfirmed media reports that 20-year-old Newtown shooter Adam Lanza enjoyed a range of video games, from the bloody “Call of Duty” series to the innocuous “Dance Dance Revolution.” But the same could be said for about 80 percent of Americans in Lanza’s age group, according to the Pew Internet and American Life Project. Law enforcement officials haven’t made any connection between Lanza’s possible motives and his interest in games.

The video game industry has been mostly silent since Friday’s attack, in which 20 children and six adults were killed. The Entertainment Software Association, which represents game publishers in Washington, has yet to respond to politicians’ criticisms. Hal Halpin, president of the nonprofit Entertainment Consumers Association, said, “I’d simply and respectfully point to the lack of evidence to support any causal link.”

It’s unlikely that lawmakers will pursue legislation to regulate the sales of video games; such efforts were rejected again and again in a series of court cases over the last decade. Indeed, the industry seemed to have moved beyond the entire issue last year, when the Supreme Court revoked a California law criminalizing the sale of violent games to minors.

The Supreme Court decision focused on First Amendment concerns; in the majority opinion, Justice Antonin Scalia wrote that games “are as much entitled to the protection of free speech as the best of literature.” Scalia also agreed with the ESA’s argument that researchers haven’t established a link between media violence and real-life violence. “Psychological studies purporting to show a connection between exposure to violent video games and harmful effects on children do not prove that such exposure causes minors to act aggressively,” Scalia wrote.

Still, that doesn’t make games impervious to criticism, or even some soul-searching within the gaming community. At this year’s E3 — the Electronic Entertainment Expo, the industry’s largest U.S. gathering — some attendees were stunned by the intensity of violence on display. A demo for Sony’s “The Last of Us” ended with a villain taking a shotgun blast to the face. A scene from Ubisoft’s “Splinter Cell: Blacklist” showed the hero torturing an enemy. A trailer for Square Enix’s “Hitman: Absolution” showed the protagonist slaughtering a team of lingerie-clad assassins disguised as nuns.

“The ultraviolence has to stop,” designer Warren Spector told the GamesIndustry website after E3. “I do believe that we are fetishizing violence, and now in some cases actually combining it with an adolescent approach to sexuality. I just think it’s in bad taste. Ultimately I think it will cause us trouble.”

“The violence of these games can be off-putting,” Brian Crecente, news editor for the gaming website Polygon, said Monday. “The video-game industry is wrestling with the same issues as movies and TV. There’s this tension between violent games that sell really well and games like ‘Journey,’ a beautiful, artistic creation that was well received by critics but didn’t sell as much.”

During November, typically the peak month for pre-holiday game releases, the two best sellers were the military shooters “Call of Duty: Black Ops II,” from Activision, and “Halo 4,” from Microsoft. But even with the dominance of the genre, Crecente said, “There has been a feeling that some of the sameness of war games is grating on people.”

Critic John Peter Grant said, “I’ve also sensed a growing degree of fatigue with ultra-violent games, but not necessarily because of the violence per se.”

The problem, Grant said, “is that violence as a mechanic gets old really fast. Games are amazing possibility spaces! And if the chief way I can interact with them is by destroying and killing? That seems like such a waste of potential.”

There are some hints of a growing self-awareness creeping into the gaming community. One gamer — Antwand Pearman, editor of the website GamerFitNation — has called for other players to join in a “Day of Cease-Fire for Online Shooters” this Friday, one week after the massacre.

“We are simply making a statement,” Pearman said, “that we as gamers are not going to sit back and ignore the lives that were lost.”