From the time Mr. Fonda made his first Broadway and television appearances in the early 1960s, his looks and style — piercing blue eyes, firm jaw and imposing frame — were inevitably compared to his father’s, and it seemed that he might be the breakout star of his generation. But his career cooled — while that of his sister, Jane Fonda, flourished — and his next appearance on the list of Oscar nominees was in 1997 for “Ulee’s Gold.” He was nominated for best actor for his role as a widowed beekeeper with grandchildren.

[Want to see some of Fonda’s best? Here are 7 great movies to stream.]

“Peter is all deep sweetness, kind and sensitive to his core,” Jane Fonda wrote in “My Life So Far,” her 2005 memoir. “He would never intentionally harm anything or anyone. In fact, he once argued with me that vegetables had souls. It was the ’60s.”

Peter Henry Fonda was born on Feb. 23, 1940, in Manhattan, the younger of two children of the film star Henry Fonda and Frances Seymour (Brokaw) Fonda, a New York socialite. His mother committed suicide in 1950, when he was 10 and Jane was 13.

Less than a year later, Mr. Fonda shot himself in the stomach with a pistol. Interviewed by The New York Times decades later, he insisted that it was an accident, not a suicide attempt or even a warning. “You shoot yourself in the hand or foot if you want attention,” he said, “not the way I did.”