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8 year oldKeith Lamont Scott exited his car with a handgun when officers opened fire, said Charlotte-Mecklenburg Police Chief Kerr Putney.
Mr Scott, a 43-year-old black man, was shot by a black officer and died in hospital.
His death sparked overnight protests, leaving 16 officers injured.
Chief Putney said Mr Scott first got out of the car with a gun and got back in when officers directed him to drop his weapon.
As he got out again, officers shot him.
"It's time to change the narrative, because I can tell you from the facts that the story's a little bit different as to how it's been portrayed so far, especially through social media," he said.
Chief Putney added that officers did not find a book at the scene, contradicting claims by Mr Scott's family that he was reading a book in his car when he was shot.
He added while it was evident Mr Scott was armed, it was unclear whether he was pointing the weapon at officers.
Officer Brentley Vinson, a two-year veteran who shot Mr Scott, has been placed on administrative leave over the incident.
Charlotte police were looking for a different suspect to serve a warrant at a block of flats when Mr Scott was killed, police spokesman Keith Trietley said.
When police saw Mr Scott leave the car with a gun, they deemed as a threat and opened fire.
He died later at Carolinas Medical Center.
At a subsequent news conference of black leaders, a Nation of Islam leader called for an economic boycott of Charlotte.
BJ Murphy said: "We don't got nothing to lose."
Mayor Jennifer Roberts, meanwhile, called for calm after protests convulsed the city overnight.
Police used tear gas on dozens of protesters and arrested one in the unrest, which shut down part of Interstate 85.
Following the shooting, a woman who claimed to be Mr Scott's daughter posted a video to Facebook saying her father was unarmed and had a disability, the Charlotte Observer reports.
She claimed Mr Scott was unarmed and reading while he was waiting for his son's school bus and was tasered before being shot four times.
Police have not responded to her claims and her account could not be immediately verified.
The protests came a day after police in the city of Tulsa, in Oklahoma, said a black man they had killed on Friday was unarmed.
The North Carolina and Oklahoma incidents are the latest in a string of police shootings that has gripped the US and led to mounting racial tensions across the country.
Mr Scott's family plans to hold a news conference later on Wednesday in the area where he was shot.
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