The incident started around 8 a.m. when an officer stopped a vehicle on Sourwood Drive, near Veanna Drive behind Westarea Elementary School for a window tint violation.
According to police, Officer Phillip Burlingame - who made the stop - called for backup because the occupants of the vehicle were acting suspiciously, and Officer Denton Little came to help him.
Burlingame then asked the driver - 24-year-old Antoine Morrell Willis - to step out of the car so he could be searched. Police say Willis began struggling with Burlingame.
When the struggle began, police say the passenger in the car - 20-year-old Lawrence Edward Graham III - got out of the car and ran. Officer Little gave chase.
Investigators say Graham had a gun and displayed it as he turned towards Officer Little, who felt threatened, fired three shots, striking Graham twice in the back.
"At some point during that encounter that individual he believed was pointing or beginning to point the gun at him," Fayetteville Police Chief Harold Medlock said.
As for if Graham was a threat if he was shot in the back, Medlock said it was still early in the investigation and all the facts are not known.
"When someone is dynamically moving and then when they are shot are usually two different things. From the time that bullet leaves the barrel of a gun someone who was doing something, could have been doing something else," he explained.
"One thing that I'm trying not to do with you today is hide any of the facts from you," Medlock added. "What I'm giving you are the facts at this point and I'm not going to suppose anything."
Medlock told ABC11 that he believed police cruiser dash cam recorded the entire incident, but that he had not reviewed the tape yet.
During the incident, Westarea Elementary School was placed on lockdown for a brief time, as a precaution.
Neighbor Tremel Dillahunt said he heard the gunshots, then went outside, and witnessed the officers yelling at the injured man.
"'Don't move, stay down and put it down,' but I'm not sure if he had anything at the time," Dillahunt said.
Graham was taken to Cape Fear Medical Center in unknown condition. Willis is charged with possession of the drugs ecstasy and marijuana with intent to distribute and resisting arrest.
The SBI is investigating the incident.
Officers Little and Burlingame have been placed on administrative leave. Police officers are routinely placed on administrative leave while investigations into officer involved shootings are ongoing.