"We have requested the government of Tamil Nadu to intervene and stop the film from releasing," Tamil filmmaker Seeman, who heads the group, told IANS after seeing the movie's trailer.
"We would like to see the film before its release as it is learnt from the trailer that LTTE (Liberation Tigers of Tamil Eelam) cadres are shown as terrorists.
"How can people who fought for Sri Lankan Tamils be shown in such poor light? We don't want to make assumptions and, therefore, request that the film be shown to us before release.
"We wouldn't allow the release of the film in Tamil Nadu until it's shown to us," he added.
"Madras Cafe", a political-thriller, is directed by Shoojit Sircar. The film deals with terrorism and civil war and was reportedly shot in Sri Lanka and India.
Seeman says his party will urge Tamils not to watch the film.
"It has become a fad to show LTTE members as terrorists in cinema. Thousands of Tamils were killed in Sri Lanka during the 2009 genocide. Why doesn't anyone make a film on the genocide?
"If we don't find any scene in the film objectionable, then we will be more than happy to allow its release. I hope the government will get in touch with the producers and come to an amicable agreement."
"Naam Thamizhar" was originally founded by S.P. Adithanar. Since the 2009 genocide, Seeman has headed it.
"Madras Cafe" also features Ayushmann Khurana, Nargis Fakhri, Rashi Khanna and Leena Maria.