Duval County Schools Superintendent Diana Greene said the man tried to get into Ruth Upson Elementary School through two different doors, First Coast News reported. The school was then locked down.
A school safety assistant followed the man off campus to a nearby church, where Duval County Schools police officers confronted him. Police said they ordered the man to drop the ax, but he refused and was shot once by an officer.
Police later identified the man as 37-year-old David Hurley, according to First Coast News. He remained hospitalized in critical condition Saturday.
Hurley faces charges of assault with a deadly weapon without intent to kill, trespassing on school property with a firearm or other weapon, and aggravated assault on a law enforcement officer, first responder or security guard.