Two former wives and a son talk to Larry King about life with John Allen Muhammad tonight at 9 ET.
Washington (CNN) -- The Supreme Court refused Monday to block the execution of John Allen Muhammad, the mastermind of the sniper team that terrified the suburbs of the nation's capital in October 2002.
Known as the D.C. Sniper, Muhammad is scheduled for execution Tuesday evening at a state prison near Jarratt, Virginia.
Muhammad, 48, has continued to profess his innocence during two lengthy trials, including one featuring testimony from young accomplice Lee Boyd Malvo, whom Muhammad referred to as his "son."
With the Supreme Court denying his appeal, Muhammad, 48, is all but sure to die by lethal injection at 9 p.m. ET Tuesday at the Greensville Correctional Center.
The only remaining issue is a clemency petition to Virginia Gov. Tim Kaine, who has indicated that he is not apt to grant it.
Lawyers for Muhammad also could file additional appeals, although it is not clear on what grounds.
Prosecutors say Muhammad, fueled by grudges against the Army and his ex-wife, plotted a cross-country shooting rampage, culminating in a killing spree in Washington.
During three weeks in October 2002, Muhammad and Malvo killed 10 people and wounded three while taunting police with written messages and phoned-in threats and demands. In notes left at shooting scenes, the snipers demanded $10 million to stop the shootings.
Prosecutors say Muhammad intended the killings to provide a smokescreen to cover up his real goal: He hoped to kill his wife, Mildred, and gain custody of his three children.
Defense attorneys and some supporters say Muhammad is mentally ill and suffered post-traumatic stress disorder during his service in the Persian Gulf War.
Muhammad was convicted of capital murder and terrorism charges in Virginia for killing Dean Harold Meyers, a Vietnam veteran cut down by a single bullet as he filled his gas tank at a Manassas, Virginia, service station.
Muhammad also stood trial in Maryland and was convicted of six murders there.
Malvo was tried in Virginia for the October 14, 2002, murder of FBI analyst Linda Franklin, 47, outside a Home Depot in Fairfax County, Virginia. A jury sentenced Malvo to life in prison after defense attorneys said Malvo, who was 17 at the time of the murders, was brainwashed by Muhammad.
Malvo testified against Muhammad at Muhammad's Maryland trial, calling him a "coward."
CNN's Jean Meserve and Mike Ahlers contributed to this story.