Abu Hamza is in custody in New York awaiting trial on charges of bombing two United States embassies in Africa.
The radical cleric touched down in America on Saturday after he was kicked out of the UK following a failed appeal against extradition at the High Court on Friday.
Within hours of landing, the former imam at the Finsbury Park mosque in north London found himself in a Manhattan courtroom facing terror charges, but he did not enter a plea or make an application for bail during the brief hearing.
Hamza arrived in court without the hook he uses as a hand, and complained through his lawyer that he wanted it to be given back. He was jailed in the UK for seven years for soliciting to murder and inciting racial hatred in 2006, first faced an extradition request from the Americans in 2004.
He has been charged with 11 counts of criminal conduct related to the taking of 16 hostages in Yemen in 1998, advocating violent jihad in Afghanistan in 2001, and conspiring to establish a jihad training camp in Bly, Oregon, between June 2000 and December 2001.
Four other men - Khaled Al-Fawwaz, Adel Abdul Bary, Syed Ahsan and Babar Ahmad - who also had last-ditch extradition challenges thrown out in London, pleaded not guilty to other terror charges.
Ahmad, a computer expert from south London, and Ahsan are accused of offences including using a website to provide support to terrorists and conspiracy to kill, kidnap, maim or injure persons or damage property in a foreign country. They were arraigned in New Haven in Connecticut.
Bary and Al-Fawwaz were allegedly involved in, or supported, the bombing of US embassies in Nairobi and Dar es Salaam in 1998. They appeared alongside Hamza in New York.
US Attorney Preet Bharara called the extraditions "a watershed moment".
The High Court ruled on Friday that the five men had lost their grounds for appeal and within hours they were placed on flights to the US. They had been fighting extradition for between eight and 14 years.