Rayshard Brooks, 27, was shot dead as he fled officers in a restaurant car park in Atlanta late on Friday.
The killing sparked protests. A top House Democrat said Mr Brooks' actions "did not call for lethal force" - echoing a statement by Atlanta's mayor.
The city's police chief has quit and the officer involved has been fired.
Atlanta is one of many US cities where the killing of George Floyd by Minneapolis police has sparked protests against racism and police brutality.