New York Police Department Commissioner William Bratton said Friday that the NYPD has "a very good idea" of who was involved with replacing the American flags atop the Brooklyn Bridge with white ones more than two weeks ago.

Mr. Bratton addressed the prank, which some viewed as a serious security threat, on "CBS This Morning." When asked why the NYPD hasn't made an arrest in the case, which has prompted the agency to increase security on the iconic bridge, Mr. Bratton said "knowing's not proving."

"So when we have the proof, we'll move. We've put, as you might appreciate, exhaustive efforts into this investigation," he said.

Critics called into question how anyone could have pulled off the complex July 22 stunt even in the middle of the night, since the department has officers stationed on each end of the bridge.

The incident prompted the NYPD to examine how it provides security on the bridge and other thoroughfares, a law-enforcement official said. The NYPD's deputy commissioner of intelligence, John Miller, even scaled the bridge several days after the incident to investigate.