His death was announced by Sony Pictures Entertainment, which did not give a cause.

Mr. Calley — three-time studio chief, confidant of Stanley Kubrick, producer of “The Da Vinci Code” — rose to Hollywood’s highest ranks not by slashing and burning but by making gut-level bets on directors and writers, and by gently and quietly steering them.

“Working with him is like rolling in feathers,” the screenwriter Jay Presson Allen said in a 1994 New Yorker article.

Stints leading Warner Brothers, United Artists and Sony gave Mr. Calley his A-list status in Hollywood’s executive ranks, but it was his approach to those jobs that made him stand out. Rather than cranking out franchise films and other safely commercial fare — a common complaint about studios today — Mr. Calley believed that successful moviemaking boiled down to one thing: making good films.

Like any studio boss, he had his share of failures and purely commercial hits. (One of his hits was “The Towering Inferno.”) But he also shepherded admired films like “A Clockwork Orange” (1971), “The Exorcist” (1973), “Chariots of Fire” (1981) and “As Good as It Gets,” a 1997 film that won Oscars for Jack Nicholson and Helen Hunt.

“When he believed in someone, he trusted and supported him,” Mike Nichols, whose collaborations with Mr. Calley ran from “Catch-22” in 1970 to “Closer” in 2004, said in a statement. “When very rarely he had a suggestion, it was usually a lifesaver.”

Mr. Calley, who had a habit of leaning back in office chairs and propping his feet up on desks and coffee tables, was notable for his lack of pretension, said Amy Pascal, Sony’s current co-chairwoman, who worked on hits like “Men in Black” with him.

“He had a sense of humor about himself and never started to think it was about him — it was about the movies and the directors,” Ms. Pascal recalled in a telephone interview.

John Calley was born July 8, 1930, in Jersey City, the son of a car salesman, and, after serving in the Army, worked at 21 as a mail clerk for NBC in New York. After climbing a few rungs on the network’s ladder, Mr. Calley left to join an advertising firm before giving film producing a try at Filmways, a production company mostly known for TV comedies like “The Beverly Hillbillies.”

He delivered a string of culturally important films there, including satirical examinations of war, like “The Americanization of Emily” (1964) and “Catch-22,” which identified him as part of a seismic shift in Hollywood’s balance of power toward a new generation of young filmmakers.

“Kids were kings,” Mr. Calley said in a 1999 interview with The Los Angeles Times. “We were all young, it was our time, and it was very exciting.”

Soft-spoken and cerebral, Mr. Calley in 1969 moved to Warner Brothers, where he ultimately served as chairman. During this time he helped make “Mean Streets,” “All the President’s Men” and “Superman.” But in 1980 he walked away, quitting with seven years remaining on a new contract — because, according to news reports at the time, he said he simply wasn’t having fun anymore.

He decamped to a 35-room house on Fishers Island in Long Island Sound.

He produced a movie here and there, including “Postcards From the Edge” (1990), but did not fully resurface until 1993, when the talent agent Michael Ovitz engineered Mr. Calley’s takeover of a troubled United Artists. As Mr. Calley told The New York Times in 1997, the goal was “putting rouge on the corpse” to prepare the studio for sale.

United Artists, owned by Metro-Goldwyn-Mayer, soon delivered hits like “The Birdcage” and the critical darling “Leaving Las Vegas.” The unit was never sold.

In 1996 Mr. Calley took the reins of Sony’s movie operation, which was reeling from overspending, executive infighting and an uneven performance at the box office. He again delivered hits, including “Jerry Maguire” with Tom Cruise, but his biggest contribution to the studio involved restoring stability: Columbia, Sony’s major arm, had four presidents come and go from 1991 to 1996.

He stepped down in 2003 but kept producing movies for Sony, including “The Da Vinci Code,” which drew more than $758 million at the global box office.

Mr. Calley’s survivors include his daughter, Sabrina Calley, and three stepchildren, Emily Zinnemann, David Zinnemann and Will Firth, from his marriage to the actress Meg Tilly, which ended in 2002.

Mr. Calley was startlingly honest, at least by show business standards. In 2009, when the Academy of Motion Picture Arts and Sciences gave him its Irving G. Thalberg Award for lifetime achievement, he did not attend because of illness but appeared in a video.

“You’re very unhappy for a long period of time,” he said in the video, reflecting on a movie executive’s life. “And you don’t experience joy. At the end you experience relief, if you’re lucky.”

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