Rebhorn, who had skin cancer, died at his home in South Orange, New Jersey, his agent Dianne Busch said.
His career spanned five decades and saw him appear in TV shows including The Good Wife and 30 Rock, and films such as My Cousin Vinny, Carlito’s Way and Basic Instinct.
Diagnosed with melanoma in 1992, he continued working until last month.
His agent told The Hollywood Reporter: “He fought it all this time.
“He died Friday afternoon at his home in New Jersey, where he had been receiving hospice care for a week and a half.”
He had more than 100 screen credits, one of the most recent being for Homeland, in which he played Frank Mathison, the father of Claire Danes’ CIA officer Carrie Mathison.
His films included The Talented Mr Ripley, in which he played a shipping magnate, Meet the Parents and The Game.
Rebhorn often played authority figures, including the headmaster in 1992’s Scent of a Woman and the US secretary of state in the 1996 blockbuster Independence Day.
The Philadelphia-born actor also worked on stage, with theatre roles including Broadway productions of 12 Angry Men and Our Town.
Tributes have been paid to the prolific character actor.
Actor Jason Alexander, who played George Costanza in the long-running US sitcom Seinfeld, tweeted: “RIP James Rebhorn, a lovely man and a terrific actor.”
Rebhorn played the role of a district attorney in the show’s last-ever episode.
Actor Tom Arnold wrote on Twitter: “RIP. This actor was amazing. You didn’t know him but trust me, you knew him.”
Actress Frances Fisher wrote: “Shocked and saddened to hear of James Rebhorn’s passing. Jim was a consummate actor with whom I had the pleasure to work when we were young.”
Rebhorn is survived by his wife Rebecca Linn and two daughters.