Jaffrey's death was announced by his niece Shaheen Agarwal on Facebook on Sunday. She did not give any details.
The TimesNow television news channel said Jaffrey died in London on Sunday.
In a tweet on Monday, Indian Prime Minister Narendra Modi described Jaffrey as "a multifaceted actor whose flair and versatility will always be remembered."
Jaffrey's other international films included "The Jewel in the Crown," ''Chicken Tikka Masala," ''The Man Who Would Be King" and "Death on the Nile."
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