The only US case related to the September 11 attacks was handed to the jury on Monday after District Judge Leonie Brinkema gave them roughly an hour of instructions.
In closing arguments, assistant US attorney David Raskin asked the jury to decide to execute Moussaoui, who said he would have participated in the September 11 attacks if he had not been arrested the previous month on immigration charges.
"Let me be blunt, ladies and gentlemen," said Raskin. "There is no place on this good Earth for Zacarias Moussaoui."
But one of the court-appointed defence lawyers, Gerald Zerkin, urged the jury to instead make a decision that "requires some courage" and sentence Moussaoui to life in prison.
"He wants you to sentence him to death. He came to America to die in jihad and you are his last chance," Zerkin said. "He clearly sees that as his last way to martyrdom."
The jury will just decide the sentence since Moussaoui has pleaded guilty to six conspiracy counts relating to the September 11 plot.
Moussaoui, 37, sat in the courtroom staring at the 12-member jury during most of the closing proceedings. But as he left for a morning break, Moussaoui said, "You'll never get me, America. Never ever."
After the jury left to begin deliberations, Brinkema praised both teams of lawyers and noted that the defence - with whom Moussaoui will not speak - had an "impossible client."
The prosecution showed pictures
of death and destruction
"There never has been a defendant as difficult as this one," said Brinkema.
Prosecutors earlier dismissed defence claims that Moussaoui was mentally ill and that he sought martyrdom.
Raskin said Moussaoui was "elated that al Qaeda murdered 2,972 innocent people on September 11."
"Enough is enough," Raskin said. "It is time to put an end to his hatred and venom. It is time to sentence Zacarias Moussaoui to death."
The panel of nine men and three women must be unanimous in order to sentence Moussaoui to death.
The same jury already decided that Moussaoui was eligible for the death penalty in four days of deliberations earlier this month, arguing he was responsible for deaths of that day (September 11) even though he was in jail hundreds of miles away.
That qualified him for the death penalty. The question now before the jurors is whether he deserves to die.
Zerkin said the US government was offering Moussaoui as a "sacrificial lamb."
"This is about history, it is about how our justice system responded to the worst terrorist attack on our soil."
Gerald Zerkin, defence lawyer
"The government opts for retribution against the only person it has brought to trial in relation to 9/11," the lawyer said in describing Moussaoui as an inept al-Qaeda operative.
The jury is considering evidence presented during two weeks of testimony by survivors and family members of victims of the hijackings that killed about 3,000 people in New York, Pennsylvania and at the Pentagon near Washington not far from the federal courthouse.
Prosecutors showed pictures of charred bodies and a video clip of people jumping from New York's World Trade Centre during their closing arguments.
Zerkin said the government was trying to assuage the families' pain by pressing for Moussaoui's execution.
"If the people who testified ... need the death of Mr. Moussaoui to recover, it can only be because the government has held that out for them," he said. "The government has held out the prospect of Mr. Moussaoui's execution as being the cure."
Zerkin also asked jurors to note that in history even in the Nuremberg trials after the second world war, only 11 death sentences were handed out for "the worst atrocities in the history of man."
He said Moussaoui was "a veritable caricature of an al-Qaida terrorist" and "the only al-Qaida operative inept enough to be captured before 9/11."
"This is about history, it is about how our justice system responded to the worst terrorist attack on our soil," Zerkin said.
Defence lawyers tried again to have the death penalty stricken from the case, based on their inability to put direct questions to witnesses held elsewhere as enemy combatants.
But Brinkema dismissed that motion, agreeing with the prosecution that the issue had already been decided by an appeals court.
Moussaoui testified twice in the trial. He contradicted previous statements by saying he was meant to pilot a fifth plane into the White House as part of the hijacking plot, though the government offered nothing to support that claim.
The 37-year-old French citizen also said he wished more Americans could have suffered in the attacks.