The aircraft, United Airlines Flight 93, crashed in a field in the state of Pennsylvania after passengers apparently fought back against the hijackers.
Hamdan allegedly heard bin Laden say that the aircraft was heading for "the dome", an apparent reference to the US Capitol building, Navy Lieutenant Commander Timothy Stone said.
|Hundreds of detainees are still being held in Guantanamo Bay [EPA]
Hamdan, who has been held at the US military prison in Guantanamo Bay in Cuba for more than six years, is charged with conspiracy and aiding terrorism.
He has pleaded not guilty to the charges and could face life in prison if convicted.
Hamdan was part of a small circle of loyal employees under bin Laden who admired the al-Qaeda leader and who enjoyed his absolute confidence, the agent, Ali Soufan, said.
Al Jazeera's Monica Villamizar, who is attending the trial at Guantanamo Bay, said the agent gave a detailed account in which he also presented several photos including images purporting to show Hamdan was armed and standing close to bin Laden as evidence that he was part of bin Laden's inner circle.
However the defence said this did not prove Hamdan was actually guilty of conspiracy, our corresponsdent reported.
The atmosphere was often very tense in court, with Hamdan at times seeming stressed and consulting his lawyers and interpreter as Soufan testified, our correspondent added.
Hamdan later protested the showing of a video of his interrogation by US authorities, walking out of the courtroom.
"Mr Hamdan does not want to watch the video," one of his lawyers told the military officer presiding over the trial.
The video shows Hamdan with a thick beard two days after his capture in Afghanistan in November 2001.
In poor quality footage, he is shown kneeling on the floor under armed guard with his hands cuffed, struggling to answer a barrage of questions about items allegedly found in the car he was driving, including two surface-to-air missiles.
'No significant role'
Hamdan's defence lawyer, Harry Schneider, has said that his client was merely an employee of bin Laden's and had no significant role in the attacks, widely thought to have been committed by the al-Qaeda network.
Captain Keith Allred, the military officer presiding over the tribunal, had earlier dealt a blow to the prosecution by ruling they could not use some evidence because it was obtained in "coercive" conditions when Hamdan was held in Bagram, Afghanistan, after his capture in 2001.
The judge also left open the possibility of throwing out other evidence from an interrogation in 2003.
However he rejected demands from defence lawyers to prohibit statements made by Hamdan during his six years at the Guantanamo camp.
The judge said that as Hamdan was being held as a designated "enemy combatant" the protections guaranteed by the US constitution against self-incrimination did not apply.
Allred's decision on evidence obtained by coercive means could present difficulties in future trials at Guantanamo, including the case of Khalid Sheikh Mohammed, the alleged al-Qaeda mastermind behind the September 11 attacks.
Earlier this month five men, including Mohammed, were charged with crimes relating to the September 11 attacks.
Hamdan's trial continues.