Some members of the Rajput community have accused the director of "distorting historical facts" and portraying Rani Padmavati (played by Deepika Padukone) in bad light in the film.
The protesters have demanded that a group of historians and their group members be shown the film before its release on December 1.
In the letter to Singh, filmmaker and convenor of IFTDA Ashoke Pandit said that as the agitators have threatened to raze the cinema halls to ground, adequate protection must be provided to the "Padmavati" team.
"We are concerned with the cause of film 'Padmavati', which has become a serious issue that needs your immediate attention and stern handling of the situation, which is going out of control..."
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Calling Bhansali a "sensible" director, the letter read, "A director has his or her fundamental right of creativity, freedom of expression and has prerogative to take liberty with history... He (Bhansali) was previously man-handled at Jaipur, shooting was stopped and was even threatened for his life by the hoodlums. The mental trauma, physical threat to his life and his fears are continuously rising everyday inching towards the release of his film.
"But how (can) the Rajput community and its fringed groups of insane people blindly allege distortion of historical facts and hurting of their sentiments, when the film has not been seen by anybody?" the letter further read.
The IFTDA yesterday requested police protection for Bhansali in a letter written to Maharashtra Chief Minister Devendra Fadnavis.
The film also stars Shahid Kapoor as Maharawal Ratan Singh and Ranveer Singh as Sultan Alauddin Khilji.
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