But his defence team argued against the penalty, saying that it would turn him into a martyr.
Moussaoui, 37, a Frenchman of Moroccan background, was in jail at the time of the September 11 attacks on the US.
He is the only man so far to be tried in a US courtroom in connection with the attacks.
He pleaded guilty in April to six counts, three of which carry the death penalty, including conspiracy to commit terrorism.
"Please don't make him a hero," defence lawyer Edward MacMahon said at the start of the trial to determine Moussaoui's sentence. "He just doesn't deserve it."
'Blood on his hands'
Government lawyers said he had the blood of nearly 3,000 victims on his hands, as he had lied to investigators after his arrest, the month before the attacks when he raised suspicions at a flight school.
"Even though he was in jail on September 11, 2001, Moussaoui did his part ... as a loyal al-Qaeda soldier," said lead prosecutor Robert Spencer.
"His lies provided the operational security and allowed his brothers to go forward and kill. Had Moussaoui just told the truth on September 11, 2001, it would all have been different," he said.
"This man knew there was a ticking timebomb in the United States, he knew there was a plot that was about to unfold," said Mr Spencer.
But defence counsel Mr MacMahon said the jury must not allow Moussaoui to "live on as some smiling face in a recruiting poster for Osama bin Laden".
Long process
Moussaoui's sentence hearing, behind held in Alexandria, Virginia, is expected to last up to three months.
Twelve jurors are to decide on his fate, firstly on whether his actions directly led to at least one death on September 11.
If it finds so, another phase of the trial will be held to decide whether Moussaoui will be executed.
If spared the death sentence, he is likely to spend the rest of his life in prison.
Moussaoui, dressed in a green prisoner's jumpsuit and a white cap, spent most of his time leaning back in his chair rubbing his long, bushy beard.
In the past he has disrupted court appearances, but this time he watched with little expression and took notes.
After the judge left the courtroom, Moussaoui criticised Mr MacMahon, one of several court-appointed lawyers whom Moussaoui detests, and vowed to testify to tell his side of the story.
Hundreds of relatives of those killed in the September 11 attacks watched the trial live by video link from special courtrooms around the country, and a few were present in the courtroom.
Although Moussaoui claims he was not meant to be part of the September 11 attacks, he said Osama bin Laden had picked him to fly a plane into the White House as part of a broader conspiracy.