An executive for one of the theater chains, who also spoke on condition of anonymity, called the invocation of the 9/11 terror attacks by hackers “a game changer.” The executive last week dismissed the notion that theater owners might shy away from “The Interview” over earlier, more general threats by North Korean officials and pressure from the hackers, who have called themselves the Guardians of Peace. Nobody yet knows the hackers’ true identity.

Representatives of AMC Entertainment, Regal Entertainment and Cinemark, North America’s three largest theater chains, did not respond to queries. A spokesman for the National Association of Theater Owners, which represents exhibitors, declined to comment.

Pressure to pull the “The Interview,” which stars Seth Rogen and James Franco and is directed by Mr. Rogen and Evan Goldberg, has centered on its depiction of Mr. Kim’s assassination. To depict the killing of a sitting world leader, comically or otherwise, is virtually without precedent in major studio movies, film historians say. Mr. Rogen canceled planned publicity interviews on Tuesday.

But a broad threat of theater violence, following a sustained attack on Sony’s digital existence, is also without precedent, and opens a new range of worry for Hollywood.

As Sony and exhibitors spoke in a 2 p.m. conference call on Tuesday, they faced the concerns of competing studios, whose important holiday films will be playing side-by-side with “The Interview” in multiplexes nationwide.

A further complication is a general reluctance, even after the 2012 mass shooting at an Aurora, Colo., theater, to visibly increase security, which might create an impression that multiplexes in general are not safe and might complicate dealings with their own insurers.

It is not unusual for studios to face threats for planned releases. In 2012, Sony was peppered with less specific threats related to “Zero Dark Thirty,” about the killing of Osama bin Laden. It opened largely without incident. Universal Pictures in 1988 was besieged by angry protesters when it released Martin Scorsese’s “The Last Temptation of Christ,” with its depiction of an earthy Jesus; more than a dozen people were injured when Christian opponents of the film firebombed a Paris theater showing the movie.