The cause of death was not disclosed. The New York Times reported
that Gaynes died at his daughter's home in North Bend, Washington.
Gaynes, known for his leading-man good looks and rich baritone voice (in fact, he came to America from Europe to sing opera), had been a Hollywood and stage fixture for decades, often playing authority figures such as doctors, professors and law-enforcement officials. He finally broke through in 1982's "Tootsie," in which he played John Van Horn, a lecherous actor (who portrayed, of course, a doctor in the film's fictional soap opera).
Two years later he expanded his audience with his appearances in "Police Academy" and "Punky Brewster."
In the former he played the buffoonish commandant, a role he would reprise in the franchise's other six films.
In the latter, a series that ran from 1984 to 1987, he was a curmudgeonly building manager who finds an abandoned girl, played by Soleil Moon Frye, and eventually becomes her foster parent.
Frye remembered Gaynes on Twitter and Facebook Tuesday night.
"The universe just gained a gigantic star. You will be in my heart and soul always & forever. Your little Punky," she tweeted.
Gaynes said that creating his character, Henry Warnimont, took some time.
"It turned out he was basically a very kind and generous man, which he covered up with his surface gruffness and his surface blusteriness," he said in an interview
. "We had a good time doing it."
The children were fine to deal with, he added, but "you learn to stay away from the mothers. I would do a scene and go to my dressing room fairly rapidly and close the door."
Gaynes appreciated the recognition his new stardom brought, though he was careful to note that he'd had quite a career before the '80s came along.
"The general public seems to think that my career consists exclusively of 'Punky Brewster,' 'Police Academy' and 'Tootsie.' But I've done quite a lot more than that," he said, noting that he did opera and Broadway at the same time in the 1950s.
His Broadway credits include "Wonderful Town," with Rosalind Russell, "Any Wednesday," whose cast included Gene Hackman, and a revival of "Gigi."
He was also a frequent TV guest star, appearing in such series as "Mission: Impossible," "Columbo," "The Six Million Dollar Man" and "Quincy." He had significant roles in the series "The Days and Nights of Molly Dodd" and "Hearts Afire."
His other movie credits include 1973's "The Way We Were," 1983's "To Be or Not to Be," 1994's "Vanya on 42nd Street" and 1997's "Wag the Dog."
Gaynes was born in Finland in 1917 and raised in western Europe.
Aside from his daughter and extended family, he is survived by his wife of 62 years, Allyn Ann McLerie. According to The New York Times, a son died in a 1989 car crash.