"I am deeply saddened to learn that the veteran stage and film actor has passed away," the prime minister said in a condolence message to Puri's family and to "the millions of his admirers".
"Puri made a mark on stage and went on to become one of the most recognisable faces in Hindi cinema as well as among international audiences.
"His portrayal of such diverse roles as in Shyam Benegal's 'Nishant' and 'Bhumika', the villain Magambo in 'Mr. India' and the grandfatherly widower in 'Chaachi 420' endeared him to a wide range of cinema viewers across generations," he said.
"Indian cinema and theatre will without doubt miss his commanding an endearing presence," he added.