The cleric would “dispatch men around the world for war” from the North London venue to kill non-Muslims and support al-Qaeda, it was said.
Hamza also used the cover of Islam to continue recruiting for Osama bin Laden under the noses of British authorities.
Setting out the case to the jury, prosecutor Edward Kim said: “War was his cause and it was all-consuming.”
Mr Kim said: “His goal was clear. It was simple, it was violent: all able-bodied men have a duty to wage war against non-Muslims, a duty to fight and a duty to kill.”
The 56-year-old accused sat impassively as Mr Kim outlined the case against him at Manhattan’s Federal Court.
Mr Kim said that Hamza, who was born in Egypt but is a naturalised British citizen, was “not just a preacher of religion but he was a trainer of terrorists”.
Describing how Hamza “didn’t just talk the talk, he walked the walk”, he told how he was a key figure for al-Qaeda in Britain during the 2000s.
By portraying himself as a community imam, Hamza used the cover of religion to hide in plain sight in London, giving him years to spread al-Qaeda’s evil message, the prosecutor said.
Mr Kim said: “The [Finsbury Park] mosque was his headquarters for the global export of violence and terror. It was here that he recruited men. It was here that he indoctrinated them and it was from there that he deployed men.”
Mr Kim led the jury through the 11 counts Hamza is charged with, which date back 16 years. He explained how Hamza helped in the taking of 16 hostages in Yemen in 1998 by buying the kidnappers a satellite phone.
Hamza is also accused of conspiring to establish a jihad training camp in Bly, Oregon. In his dramatic first comments to the jury, Mr Kim said: “In the fall of 1999, two men were sent on a mission. They were directed to travel halfway across the world.
“They were sent on a mission by their leader, this man, the defendant, known to his followers as Abu Hamza. The defendant sent his men to a remote camp. Their mission was simple: to establish a training camp, a training camp for terrorists.”
Mr Kim explained the men did as instructed and bought knives and explosives and set up patrols at night. He said: “Where was this camp? Where did Abu Hamza send his men to train others to fight and to kill? He sent them to our country, the United States.” Hamza was investigated for the Yemeni plot in 1999 by UK authorities but it was not until 2003 that the Finsbury Park Mosque was raided. He was extradited to America in 2012.
Hamza’s defence lawyer Joshua Dratel borrowed a phrase from former prime minister Tony Blair, and said Hamza saw his sermons as a “third way” that “was between Osama bin Laden on the one extreme and George W Bush on the other”.
At one point, Mr Dratel likened Hamza to Nelson Mandela and former US President George Washington because both men were considered rebels at one time.
Hamza has denied all the charges. If he is convicted, he will likely die in jail.
The trial continues.