Writers Guild of America spokesman Gregg Mitchell said Mann died Tuesday. The cause of death was not given.
Mann also won multiple Emmys, including one in 1973 for "The Marcus-Nelson Murders," which created a maverick New York police detective named Theo Kojak. The film, starring Telly Savalas, was spun off into the long-running TV series "Kojak."
In a career spanning more than 50 years as a writer, director and producer, Mann returned repeatedly to morally conscious themes, doing films for television on such subjects as Martin Luther King Jr., human rights advocate Simon Weisenthal and the Teamsters.
"Abby was brought along by great producers like Herbert Brodkin, but his passion was his own. From his earliest days as a writer, he was guided by a moral compass that never wavered," said Del Reisman, former president of the Writers Guild of America, West, and a longtime friend.
Mann was a struggling television writer in the 1950s when he became fixated on the postwar Nuremberg trials that brought to justice the top surviving leaders of the Nazi regime. His "Judgment at Nuremberg" had become a successful drama on television, and against all advice, he was determined to convert it into his first movie script.
"A lot of people didn't want it done," he commented in a 1994 interview. "People wanted to sweep the issue under the rug."
Mann persisted, and producer-director Stanley Kramer made the film with a cast that included Spencer Tracy, Burt Lancaster, Marlene Dietrich, Judy Garland, Richard Widmark, Montgomery Clift and Maximilian Schell. "Judgment at Nuremberg" was nominated for 11 Academy Awards and won Oscars for Schell and Mann. (Widmark, who played a U.S. prosecutor, died Monday at 93.)
"I believe that a writer worth his salt at all has an obligation not only to entertain but to comment on the world in which he lives, not only to comment, but maybe have a shot at reshaping the world," Mann said when he accepted his Oscar.
His other movies included "A Child Is Waiting" (starring Lancaster and Garland) about retarded children; "Ship of Fools" (with Vivien Leigh, Simone Signoret, Jose Ferrer and Lee Marvin) involving human interplay on an ocean liner; and "Report to the Commissioner" (featuring Michael Moriarty) about police corruption.
Finding film studios increasingly unwilling to tackle controversial subjects, Mann returned to television.
Other made-for-TV movies: "Skag" (1980), which became a short-run series for Karl Malden; "Murderers Among Us: The Simon Weisenthal Story" (1989); "Teamster Boss: The Jackie Presser Story" (1992); "Sinatra" (1992); and "Indictment: The McMartin Trial" (1995), which won him another Emmy.
One of his last works was 2002's "Whitewash: The Clarence Brandley Story," based on the true-life story of a man wrongly convicted of murder because of racism.
In 2001, his script of "Judgment at Nuremberg" was produced in New York by the National Actors Theater.
Mann was born Abraham Goodman in Philadelphia on Dec. 1, 1927, the son of a Russian-Jewish immigrant. He grew up in a tough factory neighborhood where he said he always felt like an outsider.
He began writing plays at Temple University and New York University.
After three years in the Army, he began writing scripts for television's Golden Age when high-quality TV dramas were in demand. His credits included "Lux Video Theatre," "Playhouse 90" and "Studio One," among many others.
Survivors include Mann's wife and son.