Los Angeles Superior Court Judge Robert Perry rejected the request, despite protests from Mehserle's attorneys that he could finish his short two-year sentence by the time his appeal case is decided, depriving him of justice.
The case was moved from Alameda to Los Angeles County due to high levels of publicity and tensions caused by the case.
Mehserle claimed he thought he was reaching for his Taser when he took out his gun and shot the unarmed Oscar Grant in the back, killing him.
The killing and subsequent case inflamed racial tensions as Mehserle was first convicted of manslaughter rather than murder, and then given the minimum sentence of two years in prison.
City News Service contributed to this story