Chopra wanted to show "Broken Horses" to the prime minister. But due to Modi's work schedule, a screening before the film's April 10 release was not possible.
Modi, however, sent a message to the filmmaker, thanking him for his invitation and wishing the movie well, Chopra's spokesperson said in a statement.
Set in the shadows of US-Mexico border gang wars, "Broken Horses" is a thriller about bonds of brotherhood, laws of loyalty and futility of violence.
The film, whose script was written by Chopra and Abhijat Joshi, stars Vincent D'Onofrio, Anton Yelchin, Chris Marquette and Maria Valverde in pivotal roles.
Chopra has written, directed as well as produced the Hollywood film a rare feat for an Indian.