Lashing out at the film-maker, he said Bhansali was "habitual of playing with public sentiments".
The state government has said it would not allow the movie's release till certain "controversial portions" are removed.
"No one has the right to take the law into own hands whether it is Sanjay Leela Bhansali or anyone else," the chief minister said.
The chief minister said if there is any action, "it will be against both the sides."
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On threats being issued to eliminate actors, Adityanath said, "Everyone should respect the feelings of each other. And I feel that if everyone has good thoughts and intentions, there would be amity in society."
The film is based on Rajput queen Padmavati.
Amid rumours that there was a romantic dream sequence between Padmavati and Alauddin Khilji's characters, various Rajput and other groups have been protesting across the country, including in Rajasthan, against the film, alleging it "distorts" history and hurts sentiments of people.