Gandolfini died while on holiday, the cable channel and Gandolfini's managers Mark Armstrong and Nancy Sanders said in a statement. No cause of death was given.
"He was a genius," said "Sopranos" creator David Chase. "Anyone who saw him even in the smallest of his performances knows that. He is one of the greatest actors of this or any time. A great deal of that genius resided in those sad eyes."
Gandolfini, who won three Emmy Awards for his role as Tony Soprano, worked steadily in film and on stage after the series ended. He earned a 2009 Tony Award nomination for his role in the celebrated production of "God of Carnage."
Gandolfini and his wife, Deborah, who were married in 2008, have a daughter, Liliana, born last year, HBO said. The actor and his former wife, Marcy, have a teenage son, Michael.
Gandolfini's performance in "The Sopranos" was indelible and career-making, but he refused to be stereotyped as the bulky mobster who was a therapy patient, family man and effortless killer.
In a December 2012 interview, he was upbeat about a slew of smaller roles following the breathtaking blackout ending in 2007 of "The Sopranos."
"I'm much more comfortable doing smaller things," Gandolfini said. "I like them. I like the way they're shot; they're shot quickly. It's all about the scripts -- that's what it is -- and I'm getting some interesting little scripts."
He played Secretary of Defense Leon Panetta in Kathryn Bigelow's Osama bin Laden hunt docudrama "Zero Dark Thirty." He worked for the '60s period drama "Not Fade Away," in which he played the old-school father of a wannabe rocker. And in Andrew Dominick's crime flick "Killing Them Softly," he played an aged, washed-up hit man.
There were comedies such as the political satire "In the Loop," and the heartwarming drama "Welcome to the Rileys.". He voiced the Wild Thing Carol in "Where the Wild Things Are" and made a rare return to the TV screen with the HBO film "Cinemate Verite."
Deploying his unsought clout as a star, Gandolfini produced (though only sparingly appeared in) a pair documentaries for HBO focused on a cause he held dear: veterans affairs.
"Alive Day Memories: Home from Iraq" (2007) profiled 10 soldiers and Marines who had cheated death but continued to wage personal battles long after their military service had ended. Four years later, "Wartorn: 1861-2010" charted victims of post-traumatic stress disorder from the U.S. invasion of Iraq all the way back to the Civil War.
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