Anyone found disrupting peace will face strict action, a senior police official said.
"Security has been tightened near cinema halls and multiplexes where the film is being shown. We do not want to take any chance. We are not letting any group assemble near movie theatres," the official said.
He said police personnel in plain clothes have been deployed to keep a watch on the crowd inside theatres, he said.
However, no untoward incident was reported in Kolkata.
Nearly 130 theatres are screening the film in West Bengal.
The period-drama, directed by Sanjay Leela Bhansali, has been marred by controversies since it went into production. Fringe Rajput groups, including the Karni Sena, have protested against the movie alleging that it distorts history and show Queen Padmini in "poor light".
The filmmakers have denied the allegations.
The Supreme Court had last week cleared the decks for the film's all-India release.
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