The fatal police shooting of an unarmed man in a Brooklyn housing-project stairwell left his neighbors in outraged shock and spurred renewed calls for a reform of NYPD practices.

“They could’ve yelled, ‘Stop! Turn around! Hands up!’ ” said Veronica Newsome, 66, a resident of East New York’s Louis Pink Houses, where Akai Gurley, 28, was killed Thursday by a shot from a rookie cop’s gun.

Police called it an accident, but state Assemblyman-elect Charles Barron suggested it was an intentional act by the cop.

“We believe he intentionally fired his weapon because he’s inexperienced and frightened, over what we don’t know,” said Barron, whose district includes the crime-ravaged Pink Houses.

Public Advocate Letitia James questioned why the rookie and his partner, also a rookie, were patrolling alone.

“In crime-ridden neighborhoods, rookie officers should never be operating on their own,” she said. “They must be paired with highly trained and seasoned police officers, a policy promulgated by Commissioner [Bill] Bratton but which has yet to be implemented citywide.”

Rep. Hakeem Jeffries called the shooting “senseless” and demanded Mayor de Blasio and Bratton “commit to a systematic change in the law-enforcement culture of this city.”

Brooklyn DA Ken Thompson promised “an immediate, fair and thorough investigation.”

“Many questions must be answered, including whether, as reported, the lights in the [stairwell] were out for a number of days,” he said.

Neighbors confirmed the lights had been out Thursday, but said it was no excuse.

“If he wasn’t armed, then the cops were at fault,” said longtime neighbor Lena Sherman.

The lights were fixed Friday, said resident Earl Greggs.

“Work doesn’t get done until someone gets killed,” he said.