Police have released video of a chase in Akron, Ohio, showing a black man Jayland Walker being shot dead, hit more than 60 times by pursuing officers.
Police believe Jayland Walker, 25, opened fire first and officers feared for their lives during the night-time traffic stop on 27 June.
Mr Walker was not armed when he ran away from his car but police say a pistol was later found inside it.
Akron’s mayor urged local people to show patience as protests began.
State Attorney General Dave Yost promised a “complete, fair and expert investigation” by the Ohio Bureau of Criminal Investigation while Akron police are holding a separate internal investigation into whether officers violated departmental rules or policies.
The eight officers involved in the shooting, seven of whom are white and one of whom is black, have been put on paid administrative leave.
A lawyer for Mr Walker’s family said officers had kept firing even after he was on the ground.
Derrick Johnson, president of the National Association for the Advancement of Colored People, described Mr Walker’s death as “murder. Point blank”.