The Washington sniper has been executed for a 2002 reign of terror that claimed 10 lives and left the US capital paralyzed in fear for three long weeks.

John Muhammad staggered into the death chamber with the aid of prison guards and offered no last-minute explanation for his random killings before being executed by lethal injection.

"I did not hear him utter a word," said prison spokesman Larry Traylor, confirming the execution and that Muhammad had refused to speak when asked for a final statement.

Muhammad, 48, was pronounced dead at 9:11 pm (0211 am Wednesday), five minutes after authorities at Greensville correctional center began administering a lethal cocktail of drugs as family members of the victims looked on.

"It is another life gone. This one was deservedly so," said Steven Moore, whose sister Linda was one of 10 people shot dead by Muhammad and his accomplice Lee Boyd Malvo.

Moore was dismissive of a statement from the family of Muhammad that talked about the executed man's son losing a father.

"Linda left children behind, too. She has a daughter, Katie, a son Thomas.... They are not going to see their mom. I don't have any sympathy for his family or for his children."

Earlier Virginia Governor Tim Kaine turned down a last-minute plea for clemency, ending any hopes Muhammad might have held of escaping his fate.

That decision came only a few hours after the US Supreme Court quashed a last-ditch appeal from the sniper's lawyers, who argued that he was mentally ill and should not be executed.

Muhammad's lawyer Jonathan Sheldon expressed his disappointment before the execution that the Supreme Court had quashed the appeal motion so quickly.

"We didn't have time to prepare sufficiently and the court, as three justices wrote, they did not have sufficient time to consider it. We consider it's just inappropriate to be rushing to execution," Sheldon told AFP.

Defense lawyers say Muhammad was not properly represented at his March 2004 trial, when his legal team did not contest his request to defend himself, and have suggested the veteran of the 1991 Gulf War suffered from Gulf War Syndrome.

Muhammad's son was among family members that visited Greensville to see him one final time.

"I don't know what he really wanted to ask, but I know he had a lot of questions he wanted to ask his dad," said Muhammad's ex-wife Carol Williams.

"It was very important for him to get in to see him. Because this is the last time," she told CNN.

Muhammad and Malvo, who was 17 at the time of the shootings and escaped the death penalty, killed one person in Washington, three in Virginia and six in the neighboring state of Maryland.

The motive remains unclear although Muhammad's second ex-wife alleges he intended to shoot her as one of his victims and reclaim custody of their three children.

Police found several notes at the scenes of the attacks. Two said "Call me God," another said, "Your children are not safe anywhere at any time" and asked for 10 million dollars to put an end to the killings.

During his October 2-22 shooting spree, Muhammad, a skilled marksman, picked off victims with a high-powered sniper rifle and scope seemingly at will.

The random killings terrified an area still living in dread of a repeat of the September 11 attacks and deadly anthrax mailings a year earlier.

People would squat down by their cars as they pumped gas, run from their vehicles into work, or just stay home.

Muhammad killed each of his victims with a single bullet fired from a distance, and was apprehended after an exhaustive manhunt by federal and local police.

He was sentenced to death in 2004 following his trial for one of the fatal shootings, that of Dean Meyers, who was killed while pumping gas at a suburban Virginia filling station.