The actor died at his residence in Mumbai this morning after a massive heart attack. He was 66.
The Prime Minister recalled Puri's long career in theatre and films, while Sonia Gandhi remembered him as a versatile actor.
"Om Puri was a gifted actor and socially conscious human being... Indian film industry has lost a pillar," Gandhi said and prayed for peace and strength to his family and admirers.
West Bengal Chief Minister Mamata Banerjee tweeted: "His acting skills were appreciated around the world. Condolences to family, friends fraternity."
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Union Minister M Venkaiah Naidu said Puri's demise is a
"big loss to the film industry. As an individual also, he was one of the finest human beings".
"Puri played many unconventional roles in movies like 'Aakrosh' and 'Ardhsatya'. He was known in the world of cinema for his roles in international films such as 'Gandhi', 'East is East' etc.
Bihar Chief Minister Nitish Kumar said the actor's death had caused an "irreparable" loss to the film industry.
"Puri was a wonderful actor... He won the national film award twice for the best actor and was awarded the Padma Shri in 1990 for his contribution to the film industry," he said in a message.
Rajasthan Chief Minister Vasundhara Raje said the "cinema world has lost a brilliant artist" in Puri.
Haryana Chief Minister Manohar Lal Khattar expressed grief over the demise of Om Puri, noting that the veteran actor was born in Ambala.
"The acclaimed actor had delivered some stellar performances. In his death the cinema world has lost one of its most loved characters," he added.
Maharashtra Governor C Vidyasagar said, "Om Puri was one of the most brilliant artists produced by the Indian film industry. He had the rare ability to infuse life in the characters portrayed by him."
"Gifted with a deep baritone voice, Om Puri played some of the most memorable roles, many of which are remembered even after the passage of several years," he said, adding that the actor was a socially committed person.
Madhya Pradesh Chief Minister Shivraj Singh Chouhan tweeted, "The death of great actor, Om Puri is an irreparable loss to the entertainment world. His role in films like Aarohan and Ardhasatya will remain unforgettable."
"Puri has enriched Bollywood cinema with his distinctive acting and has acted distinctly in Hollywood, British and Pakistani films," he said.
Punjab Chief Minister Parkash Singh Badal described Puri as "son of the soil" and a multifaceted personality.
West Bengal Governor Keshari Nath Tripathi said the acclaimed actor delivered some stellar performances in mainstream Pakistani, Indian and British Cinema apart from making a dent in Hollywood with his role in 'East is East', 'City of Joy' and 'Gandhi'.
Indian cultural world has truly lost a brilliant actor, he said.