Al-Masri is also accused of helping to set up an illegal military-style training camp in the north-west US state of Oregon and of helping to fund recruits to attend another camp in the Middle East.
Al-Masri, who was an imam at the Finsbury Park mosque in north London, has been in prison since February 2006, when he was sentenced to seven years for crimes of race hatred and soliciting to murder.
Born in Egypt but British by marriage, al-Masri is being held in the high-security Belmarsh prison in south-east London.
He was originally arrested on an extradition warrant from the US authorities in May 2004.
But the extradition process was put on hold until after his trial, which his legal team claimed was politically motivated, and an appeal against his conviction.
The path was cleared for extradition hearings when Britain's highest court ruled in January 2007 that he had no grounds for appeal.