In 1955 Mr. Graves began his career as a television series regular as the star of “Fury,” a western family adventure series about a rancher named Jim Newton, his orphaned ward and the boy’s black stallion. It ran until 1960 on NBC, helped pioneer television adventure series and solidified Mr. Graves’s TV credentials.

Some of his hundreds of television credits include “Alfred Hitchcock Presents,” “Whiplash” (1961), “The Dean Martin Show” (1970), the Herman Wouk mini-series “The Winds of War” (1983) and “War and Remembrance” (1988), “Fantasy Island” (1978-83) and “7th Heaven” (1999-2005). He served as the host or narrator for numerous television specials and performed in television movies of the week like “The President’s Plane Is Missing” (1973), “Where Have All the People Gone” (1974) and “Death Car on the Freeway” (1979).

Mr. Graves played his most famous television character from 1967 to 1973 in “Mission: Impossible,” reprising it from 1988 to 1990. He was Jim Phelps, the leader of the Impossible Missions Force, a super-secret government organization that conducted dangerous undercover assignments (which he always chose to accept). After the tape summarizing the objective self-destructed, the team would use not violence, but elaborate con games to trap the villains. In his role, Mr. Graves was a model of cool, deadpan efficiency.

Image Mr. Graves in a Geico commercial, spoofing his own image. Credit... Martin Agency

But he was appalled when his agent sent him the script for the role of a pedophile pilot in “Airplane!” (1980). “I tore my hair and ranted and raved and said, ‘This is insane,’ he recalled on “Biography” in 1997. Some of the role’s lines (“Have you ever been in a Turkish prison?”) looked at first as if they could get him thrown in jail, never mind ruining his career. He told his agent to tell David and Jerry Zucker and Jim Abrahams, the director-producers, to find themselves a comedian. He relented when the Zucker brothers explained that the secret of their spoof would be the deadpan behavior of the cast; they didn’t want a comedian, they wanted the Peter Graves of “Fury” and “Mission: Impossible.”

Mr. Graves used his familiar earnest, all-American demeanor in service of some of the comic movie’s most outrageous moments. He reprised the role of Captain Oveur in “Airplane II” in 1982.