An hourslong standoff followed, where the man was at one point "contained," according to the Clinton County Emergency Management Agency.
At one point during the standoff, the suspect, who has not been publicly identified, raised a gun toward police, said Lt. Nathan Dennis of the Ohio Highway Patrol. Law enforcement officers shot and killed him shortly after 3:45 p.m., he said.
"He succumbed to his injuries at the scene and everything remains under investigation at this time," Dennis said at a press conference.
The man attempted to breach the visitor screening facility at around 9 a.m. at the bureau's field office in Cincinnati, the FBI said in a tweet. Officials said the man was wearing body armor
After an alarm went off and special agents responded, the man fled north onto Interstate 71.
The man was armed with a nail gun and AR-15, law enforcement sources told NBC and CNN.