Earlier, two men extradited from the UK with Abu Hamza also appeared in court.
"There is a hate campaign which has taken place against me, " Mr Abu Hamza said.
Abu Hamza is unlikely to go to that prison because of his disabilities.
The US, for instance, will need to work out what facilities it is providing for Abu Hamza, given his disabilities.
The belated conviction of Abu Hamza, a rabble-rousing former imam of a mosque in Finsbury Park in north London, has fanned unease.
Mr Abu Hamza said he was a religious preacher and that it was unfortunate his comments had been taken out of context.
In London the security service, MI5, initially - and wrongly as it turned out - dismissed Abu Hamza as just a noisy troublemaker.
Nine cases, including those of Abu Hamza and Babar Ahmed, are still awaiting rulings, including two which involve allegations dating back to 1997.
Abu Hamza was convicted in 2006 in the UK of charges including soliciting to murder and stirring up racial hatred, and given a seven-year jail sentence.
She had secured the deportation of another radical cleric Abu Hamza.
Abu Hamza's lawyer says that her client remains a British citizen.
BBC: Abu Hamza-style delays source of 'fury' - Chief Justice
District Judge Katherine Forrest set a date of 26 August 2013 for Abu Hamza's trial, at which he will also face charges of abducting tourists in Yemen.
The revelation comes as the European Court of Human Rights have allowed Abu Hamza, and four other terrorist suspects, to be extradited from Britain to the United States.
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He said Mr Starmer's decision "smacks of a determined effort to extradite both these men" and said their cases were worlds apart from that of convicted terrorist Abu Hamza al-Masri.
BBC: Babar Ahmad and Syed Ahsan private prosecution rejected
Their extradition happened on the same day as the extradition of Abu Hamza so a lot of the detail got lost amid the focus on the jailed radical cleric.
Edward Fitzgerald QC, representing 48-year-old Abu Hamza, told the Court of Appeal it had been "unfair and oppressive" to launch a prosecution in 2004 over speeches made between 1997 and 2000.
On Wednesday, a High Court judge ordered that neither Abu Hamza nor another of the men, Khaled al-Fawwaz, could be extradited before an urgent hearing of potentially new material in the cases.
BBC: Abu Hamza-style delays source of 'fury' - Chief Justice
The BBC understands that Abu Hamza's application will focus on the state of his mental health - but the preacher is is also asking judges for his confiscated passport to be returned.
BBC: Abu Hamza-style delays source of 'fury' - Chief Justice
The Tories charge the government with operational incompetence: why was Abu Hamza not prosecuted for ten years, when six of the 11 counts he was convicted of fell under a law from 1861 against soliciting to murder?
Mr Keith said that a group of westerners including 12 Britons, two Americans and two Australians were abducted in Yemen in 1998, partly in order to gain the release of Abu Hamza's stepson Mohsen Ghailan and five others.
The Home Affairs Committee (1100) continues its look at the roots of violent radicalisation - the Committee spoke to Abu Hamza and other inmates at Belmarsh Prison - this session will hear from academic experts, then from David Anderson QC, Independent Reviewer of Terrorist Legislation and finally (at 12.15pm) from James Brokenshire MP, Minister for Crime and Security at the Home Office.
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