NEW YORK >> A New York City firefighter died early today battling a fierce blaze on a movie set after getting separated from his fellow firefighters in the thick smoke.

The fire started in the cellar of a former jazz club as the crew of “Motherless Brooklyn,” directed by Edward Norton, was nearing the end of its working day at 11 p.m. Thursday. Flames poured out the windows as firefighters stormed into the five-story Harlem building, dumping water on the blaze to get it under control.

Firefighter Michael R. Davidson of Engine Co. 69 was assigned to the nozzle on the lead hose-line and pushed into the burning basement.

But the blaze was too much. Firefighters had to back out, and the 15-year Fire Department veteran was separated from his colleagues. Firefighters searched desperately for him, and he was found unconscious after suffering severe smoke inhalation, Fire Commissioner Daniel Nigro said. Davidson was pronounced dead at a hospital shortly after midnight.

“Our city lost a hero,” Mayor Bill de Blasio said in a tweet before visiting the fire scene tonight. The Democrat called Davidson’s death “a heartbreaking tragedy for the entire city.”

Davidson, a second-generation firefighter, had been cited four times for bravery during 15 years on the job.

The building was being used to film the adaptation of the Jonathan Lethem novel of the same name. Norton was directing and starring, along with Bruce Willis, Willem Dafoe and Alec Baldwin.

Neighborhood resident Daquan Evans, 28, told the New York Post he saw Norton at the scene.

“He looked pretty upset,” Evans said. “This is crazy, this fire. You think a movie comes up here and it is good for the neighborhood. Not a fire … damn.”

The cause of the five-alarm fire was under investigation. The building, built in 1920, is a landmark and was home to the former St. Nick’s Jazz Pub, a venerable bar that was closed in 2011.

Neighbor Joan Adams said she saw white smoke, then black, billowing from basement windows in the front of the building. But when she went into her backyard, two buildings away, she could see flames.

“It was really scary,” she said.

The movie’s producers said crews immediately called the fire department when they noticed smoke coming into the set and other parts of the building.

“We watched firsthand with astonishment as they charged into the smoke to make sure all were safely out and then fought to contain the blaze and prevent it from spreading, putting their lives on the line as they do every day,” the producers said in a statement sending condolences to the firefighter’s family.

Background actor Ambroise Ironfence said the movie crew wasn’t using any open fire during the shoot and the building’s power wasn’t on.

“All the equipment we were using … the power came from the truck outside,” he told WCBS-TV.

The movie crew didn’t need a city film production permit to work at the building because it was a private residence. The filmmakers did need a street parking permit and had one, officials said.

The building owner’s phone number wasn’t accepting messages today; nor was the phone for a lawyer who has represented him in real-estate cases. An email message to the owner failed.

Neighbors said the movie crew had set up a sign that read “King Rooster Jazz Club” and began filming about two weeks ago. Cars from the 1950s era lined the street.

Douglas Miller, who lives across the street in a second-floor apartment, said the fire traveled fast and went all the way to the roof. He saw firefighters carry out one of their own, on a stretcher, and try to resuscitate him and give him oxygen.

“They tried to save him, but they couldn’t,” Miller said, and soon the firefighter was being rushed to a hospital.

Later Friday, Davidson’s body was taken to a suburban funeral home in a procession of fire trucks, getting somber salutes from firefighters stationed along the route.

Davidson, 37, was the son and brother of New York City firefighters. His father is now retired.

“You haven’t heard a scream until you’ve heard the scream of a mother who’s seen her son give his life to protect us,” tweeted the mayor’s spokesman, Eric Phillips.

Davidson leaves behind a wife, Eileen, and four children under 8. Neighbors described him as a salt-of-the-earth guy, a great friend, father and husband.

“He was a great guy — he went up and down and did everybody’s sidewalk in the snow. He was playing with the kids in the snow yesterday,” said Joanne Caldon.

Two other firefighters suffered burns and were in serious condition, and three others were injured, Nigro said.