Chief Cassandra Deck-Brown said the man killed was wanted on a felony drug charge.
Police haven't identified the man. But Rolanda Byrd told CNN affiliate WRAL
that the man was her son, 24-year-old Akiel Denkins.
She said police had no reason to shoot him.
"Everybody out here said he was running, didn't have a gun, (was) trying to jump a fence, and that officer shot my son seven times. For what? For nothing," Byrd told WRAL. "My son didn't have no gun on him. My son wasn't threatening that officer."
WRAL showed Byrd shouting at a police line: "What did he do to your child? What did he do to your mama?"
Police officer named
Police have not said why the officer opened fire or detailed how many times the man was shot. State authorities are conducting a criminal investigation into the shooting, and the department's internal affairs unit is also investigating, Deck-Brown said.
The police chief said such investigations are customary, adding that she will release a report to city officials with initial findings within five working days.
The officer was pursuing the man on foot Monday afternoon and trying to detain him, the police chief said.
"During the course of the pursuit, the suspect was shot and killed by the officer," she said. "Initially, it is known that a firearm was located in close proximity to the deceased suspect. That weapon, along with other elements available at the scene, will be processed."
In a statement Monday night, police identified the officer involved as Senior Officer D.C. Twiddy. The 29-year-old officer, who has worked for the department since 2009, has been placed on administrative duty pending the completion of the state's investigation, police said.
Video from WRAL showed a crowd gathering at the scene of the shooting for a vigil Monday night.
Casanova Womack, who lives in the neighborhood, told the affiliate that tensions were high in the neighborhood.
"People are just frustrated, angry, upset and disappointed," he said.
Denkins was well known in the community, WRAL reported.
'Time for change'
The Rev. Chris Jones, the pastor at a church several blocks from the shooting scene, also told WRAL that Jenkins could have been his son.
"I treated him like my son. I've fed him at my church before," Jones said. "Now, he's lying back there, dead."
At the vigil Monday night, Jones asked police why they had to kill Denkins, WRAL reported.
"If he ran from you today, you could have arrested him tomorrow. Why did you have to kill him today?"
Community leader Diana Powell said Denkins' death was a defining moment.
"They want to lock you up as a modern day slave," she said.
"It is time for change. It is time for all of us to get together and say no to the injustice."
Police body cameras
The Raleigh City Council had been due to discuss body cameras for officers Monday, but removed the item from the agenda after the shooting, the American Civil Liberties Union (ACLU) of North Carolina said.
"On a day when the Raleigh City Council was scheduled to discuss officer worn body cameras, this shooting points to the urgent need for North Carolina's second-largest city's police department to adopt this crucial technology and an accompanying policy that guarantees it will be used to promote officer accountability and transparency," acting Executive Director Sarah Preston said in a statement.
She said ACLU expressed its deepest condolences to Denkins' family and was trying to learn more details about what happened.
"What we do know is that far too many people of color are victims of wrongful targeting and excessive use of force by law enforcement officers across the country, and North Carolina is not immune to that reality."
Preston urged the State Bureau of Investigation and Raleigh Police Department to conduct a "thorough and transparent investigation."