The movie, which also stars John Abraham and Neil Nitin Mukesh, took Rs 350m (£4.42m) during its opening three-day weekend and entered the UK charts at number nine.
Kaif told ANI: "New York was really one of the most special films for me. It is an amazing story and for me it was such a connected film. I really wanted the film to do well. I am so happy that it did."
The 24-year-old actress also praised director Kabir Khan for bringing the controversial 9/11 story to the big screen.
Kaif, who recently wrapped up shooting De Dana Dan, is planning to return to London to celebrate her birthday with her family on July 16.