Officials say the firefighter was at a SFFD training facility on 19th and Folsom Street when he fell three stories, causing severe head injuries.
VIDEO: Paying respects to late SF firefighter, Jason Cortez
Firefighter dies after training incident, SFFD says
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SFFD Lt. Jonathan Baxter said the firefighter was transferred to Zuckerberg San Francisco General Hospital where he died before 11 a.m.
Lt. Baxter identified the victim as 42-year-old Jason Cortez, who had been with the department for 13 years - First as a paramedic and then a firefighter.
"This is a very trying time," Lt. Baxter said, describing Cortez as a paramedic who had been with the department since 2007 and was currently stationed in the Tenderloin.
Cortez was a firefighter-paramedic, advocate for public safety, father, husband and a son of a retired SF firefighter.
The San Francisco Fire Department released a statement saying, in part, "our hearts go out to his family and loved ones, especially his wife and two young children."
The statement went on to say that "as a mark of respect," the department's flags will be at half-staff until further notice, and ended with "Rest in peace, brother."
"He's a friend to all, he's an advocate for public safety, he's a father to two children, a husband to an amazing wife; and a child to a retired San Francisco firefighter," he said of Cortez.
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San Francisco fire officials held a procession for the fallen firefighter from the hospital to the medical examiner's office.
WATCH: SFFD hold procession for Jason Cortez
Procession for fallen SF firefighter
After the procession SFFD Fire Chief Jeanine Nicholson held another press conference.
"He has worked at station three engine three, which is the busiest fire engine in the country," Chief Nicholson said of Cortez. "So that should tell you something about him. He was a go getter. He cared about people, he loved his job. He loved the people he worked with, and he loved his family. And our job in the fire department right now is to hold one another up, to take care of his family and to complete an investigation."
SFFD fire chief remembers firefighter Jason Cortez
We did talk with a number of people who live across the street from the training facility. They told ABC7 News they didn't hear anything out of the ordinary this morning until after the accident. Neighbors say they often see firefighters high up on the ladder truck and on the stairs of the training tower, which is seven stories high.
Cal/OSHA is further investigating the incident.
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Stay with ABC7 News for the latest details on this developing story.