A Justice Department watchdog found that Attorney General William P. Barr did not initiate the removal of protesters in a park near the White House during demonstrations over George Floyd’s murder in 2020, but that his overall response during that period was “chaotic and disorganized.”

The four-year investigation covers one of the most polarizing moments of Donald J. Trump’s presidency: his decision on June 1, 2020, to walk from the Rose Garden through Lafayette Park, which federal law enforcement officers had violently cleared of protesters, for a Bible-brandishing photo opportunity at a nearby church.

Video taken that day showed Mr. Barr, known for his aggressive, hands-on management style, conferring with officials in the park just before Mr. Trump walked through.

But Michael E. Horowitz, the Justice Department’s inspector general, found that Mr. Barr was, at that moment, not in the chain of command at the scene, according to a report released Wednesday. The clearing of the park by baton-wielding officers, some on horseback, was directed by the Park Police and the Secret Service, not the Justice Department, the report added.

“We found that the decision to clear the area of protesters on the evening of June 1 was made by the U.S.P.P. and U.S.S.S. unified command at Lafayette Park and not by Barr, and that Barr did not impact the timing of the clearing operation,” Mr. Horowitz wrote in an exhaustive 168-page report that included more than 100 interviews. Mr. Barr and other top department officials declined to be interviewed.

“We determined that the unified command had already decided to initiate the clearing operation and had begun preparations to do so prior to Barr’s arrival,” he added.