The Parshuram Swabhiman Sena issued a statement, condemning the threats.
"There should be a strict action against those persons who are issuing threats to Deepika Padukone," Sena said in the statement.
Amid rumours that there was a romantic dream sequence between Rani Padmavati and Alauddin Khilji's characters, many Rajput groups and others have been protesting against the movie, alleging that it distorts history.
Director Sanjay Leela Bhansali, in a video appeal earlier this month, had stated that there was no such sequence in the movie and he was careful in depicting the "Rajput honour and dignity".
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