Washington alleges that Babar Ahmad raised money to support terrorism in Chechnya and Afghanistan via websites and emails. It plans to transfer the 31-year-old to the US.
The court had previously been told that Ahmad - an Imperial College computer worker - ran internet sites inciting murder and urging Muslims to fight in a holy war.
But the extradition case has prompted hundreds to demonstrate outside London's Bow Street Magistrates Court on Monday about the way British police have handled the case, the mistreatment of Muslim suspects held in Guantanamo Bay and the possiblity a US court might pass a sentence of execution.
Acting for the US government, prosecution lawyer John Hardy told the court on Monday that Washington was prepared to give assurances Ahmad would not face the death penalty or a US military court - a key concern of the defence lawyer Edward Fitzgerald.
But Fitzgerald argued that the assurance was invalid as it neither obliges the US president nor the US attorney-general to refrain from using their authority to order a military tribunal or permit an execution.
And a key US witness for the defence seconded the argument. US civil rights lawyer Thomas Loflin III pointed out that there is no clause in the current extradition treaty that says once a suspect is transferred to the US he must be detained according to civilian jurisdictions and not military ones.
Heart of the issue
Ahmad's wife told Aljazeera.net on Monday that Judge Timothy Workman was hearing a case that was being fought on whether her husband's transfer to the US would prejudice a fair trial.
"I have no confidence in the US justice system. But surely the issue is that a British citizen has been accused by a foreign government of committing crimes in the UK - he should be tried in the UK."
Ahmad has in fact already been arrested and interrogated twice by British police since 2003 - on both occasions he was released without charge.
"Without the requirement to present a case before requesting extradition, the US is able to accuse UK citizens and residents of all manner of heinous crimes without ever producing evidence"
professor of human rights and international law
She added that if British police -investigating in the only country where Babar has lived and worked - were unable to find evidence to prosecute him, just why should Washington have him.
"But there is no evidence - if there were, British police would surely have used it against him when they first arrested him. Washington says their evidence dates from between 1998-2003 - years before his first much-publicised and brutal nine-day interrogation in the UK.
"And the US is under no obligation to give British courts the supposed evidence against him, they will just be taking Washington's word for it that there is a case to answer.
"We know all about US justice - military courts, Abu Ghraib, Guantanamo - so I do not put much wait on Washington's assurances of a fair trial," she added.
Numerous international law experts in the UK agree with Ahmad's argument against extradition. Among them, London's Metropolitan University professor of human rights and international law.
Professor Bill Bowring said the defence was likely to point out that there was no way of knowing where the alleged evidence against Ahmad had come from.
Police escort Ahmad's relatives
outside Bow Street Magistrates
"Without the requirement to present a case before requesting extradition, the US is able to accuse UK citizens and residents of all manner of heinous crimes without ever introducing evidence," he said.
"The defence will argue that such allegations may be based on supposed information extracted through torture at Guantanamo Bay or other illegal prisons," he added.
Bowring pointed out that Ahmad faced no charges in the UK, yet the Extradition Act had deprived him of the protection of a proper trial because he was deemed an enemy of the US by its administration.
"This act is designed to be abused, and it can only add to the sense of vulnerability felt by Muslims, minorities and political activists at this time. The Extradition Act should be repealed but it seems it is here to stay."