In a statement on Friday, the chief of the Miami Police Department called the video “disturbing” and said that the sergeant had been suspended and an internal affairs investigation was underway.

“The actions of this employee were found to be inconsistent with the mission and values of our department,” Chief Jorge R. Colina said. “I would like to reassure our citizens of all faiths that we stand in solidarity with them.”

In a statement on Friday, the Miami Fraternal Order of Police identified the sergeant as Roberto Destephan, its vice president. It said that the video was “heavily edited” and that “the motive here appears to be political blackmail.”

In the video, Sergeant Destephan appeared to be standing in the doorway of the Miami Fraternal Order of Police.

John Cunill, a lawyer whose firm has represented Miami police officers and city officials, said he brought the video to the attention of WPLG, the local news station, “days ago.” He would not say how he obtained the footage.