To prepare himself for the role — a high-ranking mobster, or capo, who runs a crew of his own — Mr. Vigoda frequented the Lower East Side and other New York neighborhoods that are backdrops in the story. He told Vanity Fair that he “practically lived in Little Italy during the shoot.”

Tessio is an old friend and ally of the Godfather, Vito Corleone (Marlon Brando). But in a story that traces a classical tragic arc, he becomes a figure of disloyalty who pays a steep price for his betrayal.

He reprised the role in a flashback scene in “The Godfather: Part II” in 1974.

A year after that, Mr. Vigoda was cast as the worn-out Detective Fish on the station-house sitcom “Barney Miller,” opposite Hal Linden in the title role. Mr. Vigoda stayed with the series for two seasons, 1975-76 and 1976-77, and the opening episodes of a third, earning three Emmy nominations for best supporting actor in a comedy series. (The show continued without him until 1982.)

He was so successful that he achieved a rare television feat: appearing in his own spinoff, “Fish,” while still in the cast of the original show. “Fish” centered on the detective’s home life as the foster parent of five children of various racial and ethnic backgrounds. It ran from February 1977 to May 1978.