The jury in the trial of convicted al-Qaeda plotter Zacarias Moussaoui has retired to consider whether he is eligible for the death penalty.
Moussaoui has become known for his unpredictable testimony
Prosecutors said in closing arguments that Moussaoui had lied in custody to keep the 9/11 terror plot a secret.
But Moussaoui's court-appointed defence lawyers said he was a fantasist and al-Qaeda "hanger-on" who had no part in the attacks on New York and Washington.
Moussaoui has pleaded guilty to six counts of conspiracy to attack the US.
Defence lawyers appointed by the court had tried to stop the Moroccan-born Frenchman from testifying on the grounds that he would incriminate himself.
"Moussaoui was not involved in the 9/11 plot, no matter what he says," lead defence lawyer Edward MacMahon told the court in his closing argument on Wednesday.
"He's now trying to write a role for himself in history when in reality he's an al-Qaeda hanger-on," Mr MacMahon said.
Mr MacMahon said the US government had failed to prove beyond reasonable doubt that Mr Moussaoui had been involved in the 9/11 attacks.
However, prosecutors in the trial cited testimony given by Moussaoui on Monday to argue that he should be put to death for his role in the 11 September 2001 attacks.
"Zacarias Moussaoui came to this country to kill as many Americans as he could," prosecutor David Raskin said. "He was supposed to fly the fifth plane into the White House on September 11," he said.
The victims of the attacks, Mr Raskin said, "would be alive today if he had told the truth and that is why he is eligible for the death penalty".
Jurors must agree that Moussaoui's actions directly caused the deaths of 11 September 2001 if he is to be deemed eligible for the death penalty.
If this happens, the sentencing trial enters its second phase in which testimony will be heard from relatives of people who died in the terror attacks.
Jurors must then retire for a second time to consider whether to impose the death penalty on Moussaoui.
Should the jurors decide unanimously, after the trial's first phase, that the government has not successfully proven Moussaoui is eligible for the death penalty, he will spend the rest of his life in prison.
In the event of a hung jury, where no unanimous decision is reached after the first phase, Moussaoui could face a retrial or again, spend the rest of his life in jail.
Moussaoui is the only man to be charged in connection with the 2001 attacks.
He was arrested on 16 August 2001, three weeks before the eventual attacks, as he attempted to speed his way through a pilot's course.
Moussaoui has become well-known for his unpredictable outbursts in the witness box.
During frequent appearances before the US courts, he has sometimes contradicted earlier testimony and appeared mentally unstable.