CHICAGO — The F.B.I. director, James B. Comey, said on Friday that the additional scrutiny and criticism of police officers in the wake of highly publicized episodes of police brutality may have led to an increase in violent crime in some cities as officers have become less aggressive.

With his remarks, Mr. Comey lent the prestige of the F.B.I., the nation’s most prominent law enforcement agency, to a theory that is far from settled: that the increased attention on the police has made officers less aggressive and emboldened criminals. But he acknowledged that there is so far no data to back up his assertion and that it may be just one of many factors that are contributing to the rise in crime, like cheaper drugs and an increase in criminals who are being released from prison.

“I don’t know whether that explains it entirely, but I do have a strong sense that some part of the explanation is a chill wind that has blown through American law enforcement over the last year,” Mr. Comey said in a speech at the University of Chicago Law School.

Mr. Comey’s remarks caught officials by surprise at the Justice Department, where his views are not shared at the top levels. Holding the police accountable for civil rights violations has been a top priority at the department in recent years, and some senior officials do not believe that scrutiny of police officers has led to an increase in crime. While the department had no immediate comment on Friday, several officials privately fumed at Mr. Comey’s suggestion.