The New York City police commissioner, Raymond W. Kelly, through a top aide, acknowledged for the first time on Tuesday that he personally cooperated with the filmmakers of “The Third Jihad” — a decision the commissioner now describes as a mistake.

The film, which says the goal of “much of Muslim leadership here in America” is to “infiltrate and dominate” the United States, was screened for more than 1,400 officers during training in 2010.

Deputy Commissioner Paul J. Browne told The New York Times on Monday that the filmmakers had relied on old interview clips and had never spoken with the commissioner.

On Tuesday, the film’s producer, Raphael Shore, e-mailed The Times and provided a date and time for their 90-minute interview with the commissioner at Police Headquarters on March 19, 2007. Told of this e-mail, Mr. Browne revised his account.