Separately, a federal appeals court also has upheld the conviction, but ordered a new sentencing hearing.
Officer Daniel Faulkner was shot to death after pulling over Abu-Jamal's brother in an overnight traffic stop.
The case has drawn worldwide attention.
Prosecutors say Faulkner, 25, managed to shoot Abu-Jamal during the confrontation. A wounded Abu-Jamal, his own gun lying nearby, was still at the scene when police arrived, and authorities consider the evidence against him overwhelming.
Abu-Jamal, born Wesley Cook, has argued in numerous appeals that racism by the judge and prosecutors corrupted his 1982 conviction at the hands of a mostly white jury. Prosecutors, meanwhile, had appealed a federal judge's 2001 decision to grant Abu-Jamal a new sentencing hearing because of flawed jury instructions.
