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The Court did not comment Monday on why it refused to consider his appeal.
Muhammad is scheduled to die by injection at a Virginia prison for the slaying of Dean Harold Meyers at a gas station during a three-week spree in 2002 across Maryland, Virginia and Washington, D.C.
Muhammad and his teenage accomplice, Lee Boyd Malvo, were also suspected of fatal shootings in other states, including Louisiana, Alabama and Arizona. Malvo is serving a life sentence.
Muhammad still has a clemency petition before Virginia Gov. Timothy M. Kaine.
Muhammad's attorney, Jonathan Sheldon, says "Virginia will execute a severely mentally ill man who also suffered from Gulf War Syndrome the day before Veterans Day."
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