Paltrow, who was the head of a show business family including Oscar-winning daughter Gwyneth Paltrow, actress wife Blythe Danner and son Jake, a television director, had been traveling with his daughter in Italy in celebration of her 30th birthday when he became ill, Gwyneth's publicist Steven Huvane told The Associated Press.
AP reports American officials in Italy were notified of Paltrow's death on Thursday but on condition of anonymity, could not give the exact date of his death. They said he died in Rome.
Paltrow also directed his daughter in 2000's Duets, in which Gwyneth Paltrow got to show off her talented singing ability as a Las Vegas showgirl who hits the road in search of karoke contests with her long-lost father, played by Huey Lewis.
On being directed by her father, Gwyneth said: "I think he's the smartest person I've ever known in my life. And also he's my dad. I thought, maybe I'll work and get spoiled at the same time."
Paltrow married Tony-winning actress Danner in 1970. Danner, who recently starred in the comedy Meet the Parents, was working on her new TV series Presidio Med in Los Angeles and was not with her husband when he died.
Huvane told AP Paltrow's body would be flown back to the U.S. but funeral arrangements had not been made.