Tolkan died on Thursday in Lake Placid, New York, where he lived, his booking agent, John Alcantar, said on Saturday.
A brief obituary published on the Back to the Future website said Tolkan died "peacefully", but no cause of death was given.
In Back to the Future, Tolkan portrayed the bow tie-wearing vice principal Gerald Strickland, who eyeballed students for trouble in the halls of Hill Valley High School - in particular Marty McFly, played by Michael J Fox.
"You got a real attitude problem, McFly," Tolkan's character says in the 1985 film.
"You're a slacker. You remind me of your father when he went here. He was a slacker, too."
Tolkan also appeared in Top Gun as commanding officer Tom "Stinger" Jardian.
Near the end of the film, when Jardian asks Tom Cruise's character, Captain Pete "Maverick" Mitchell, about his choice for future duty, Mitchell replies that he wants to be a Top Gun instructor.
"God help us," Tolkan's character replies, laughing.
Born in Calumet, Michigan, Tolkan served in the Navy during the Korean War and eventually made his way to New York, where he spent a quarter century acting in theatre roles.
He was a member of the original ensemble cast of Glengarry Glen Ross.
Tolkan is survived by his wife of 54 years, Parmelee Welles.
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