The 48-year-old Muhammad is scheduled to die by injection on Nov. 10 at a Virginia prison. In court papers, his attorneys say the execution should be put off while the court considers whether his trial lawyer was ineffective.
Muhammad was convicted of killing Dean Harold Meyers at a Manassas, Va., gas station during a three-week spree in October 2002 that spanned Maryland, Virginia and the District of Columbia.
Muhammad and his teenage accomplice, Lee Boyd Malvo, were also suspected of fatal shootings in other states, including Louisiana and Alabama. Malvo is serving a life sentence.
Muhammad's lawyers also have asked Virginia Gov. Timothy M. Kaine for clemency, saying Muhammad is mentally ill and should not be executed.
In a 40-minute video to Kaine last month, attorneys, mental health experts and witnesses describe Muhammad's illness. Muhammad's attorneys claim he has brain damage, brain dysfunction and neurological deficits, as well as psychotic and delusional behavior, exacerbated by the Gulf War Syndrome he suffered as a sergeant in the first Iraq war.
They also submitted an interview with a juror who said that she would not have sentenced Muhammad to death if she had known of his severe mental illness.
The Supreme Court has banned executing the insane or the mentally disabled, measured by an IQ less than 70, established by the age of 18, and the lack of basic adaptive skills.
Kaine has said he knows of no reason he would commute Muhammad's sentence to life in prison, but that he would review the request. As a Roman Catholic he is opposed to the death penalty, but as governor he has allowed nine executions to take place and commuted one sentence - a man who he said was too mentally ill to be executed.
Kaine usually waits for a condemned inmate to exhaust all appeals before acting on a clemency request. The court could act anytime before the scheduled execution.