Haroon Aswat, 40, is accused of traveling to the United States in 1999 on a mission to set up a training camp in the remote hamlet of Bly, in the northwestern state of Oregon, to train militants who wanted to fight in Afghanistan.
Prosecutors say he was sent on the mission by radical British preacher Abu Hamza, who was convicted in New York earlier this year on 11 kidnapping and terrorism charges.
Aswat pleaded not guilty in October. He faces up to 35 years in prison if convicted.
Hamza, the former imam of Finsbury Park mosque in north London, was extradited from Britain in 2012 after an eight-year battle against extradition delayed by multiple appeals.
Aswat's October 21 extradition came despite his diagnosis with paranoid schizophrenia. He has been held in a psychiatric hospital since 2008.
Aswat was arrested in Zambia in July 2005.