"Truth, transparency brings trust," the Rev. William J. Barber II said Tuesday. "Nothing more, nothing less."
The man killed was identified as Akiel Rakim Lakeith Denkins, 24, of Raleigh, the North Carolina State Bureau of Investigation said.
As of late Tuesday morning, his mother, Rolanda Byrd, said she hadn't been called in to see the body.
Barber, who stood side by side with Byrd at a news conference on Tuesday, said he doesn't want to prejudge any investigation and declined to give a narrative of his own. Rather, he said he wants answers to what he considers pivotal questions:
• A gun was found near Denkins, but did that mean he was armed?
• Who found the weapon?
• Who did the gun belong to? Whose fingerprints are on it?
• Was Denkins running away when he was shot?
• Is there any video that shows the incident?
Barber credited Raleigh Police Chief Cassandra Deck-Brown
for calling in state investigators, as well as her stated desire "to follow the available facts and the evidence wherever they lead."
"Truth is the main antidote to unrest," the NAACP leader said. "... We can handle the truth. We've had to handle the truth for many, many years."
Dozens of protesters marched Tuesday afternoon from the neighborhood where the shooting occurred to a courthouse in downtown Raleigh. Police escorted the demonstrators as they walked along the streets, blocking traffic, CNN affiliate WTVD
Police: Man shot was wanted on a felony drug charge
The shooting happened in the middle of the day Monday, as a Raleigh officer tried "to detain an adult male suspect who was wanted for a felony drug charge."
"During the course of the pursuit, the suspect was shot and killed by the officer," police said, without elaborating on how many times the man was shot, whether he'd threatened or shot at the officer, or whether he was threatening anyone else.
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 into the shooting, according to the Raleigh department.
During Tuesday's news conference, Barber urged reporters not to "dehumanize" Denkins, who lost his life. He did not dispute that Denkins was the subject of a warrant or had an arrest record, saying, "All human beings (have) fault."
"But (neither) a warrant nor an arrest warrant is a license to kill," Barber added. "So we've got to make sure we ask the right questions."
NAACP leader points to tensions between police, African-Americans
Barber also touched on "historical tensions (that) exist between the African-American community and the police," referring to other incidents in which blacks have had sometimes fatal run-ins with law enforcement. (Denkins was black, as is Deck-Brown, Raleigh's police chief.)
"This tension is present in most cities, and Raleigh is no exception," he said. "All of us in America deal with it."
The State Bureau of Investigation's probe of this case, Barber hopes, will resolve what he characterized as "conflicts from the accounts of what happened and why."
He said he wants citizens to pay attention, but not overreact, as investigators do their jobs.
"We urge the community to be vigilant in the pursuit of justice, but not be violent toward one another," Barber said.
"This is no time to turn on each other. It's a time to turn to each other and stand together for justice."