But in his ruling, Thomas said there was a clear prima facie case against both Bary and al-Fawwaz.
He also dismissed the medical argument put forward by Bary's lawyer against extradition, saying: "It is clear to us that there has been no material change in the psychological condition of Abdul Bary."
Lawyers for Ahmad and Ahsan presented what they said was fresh evidence to support their calls for the two men to be charged with similar terrorism-supporting offenses in Britain, rather than have them face trial in the United States.
The U.S. and British governments strongly contested the five suspects' submissions.
Lawyers for the British government described the arguments as an abuse of the legal process.
Al-Masri is one of the highest-profile radical Islamic figures in Britain, where he was already sentenced to seven years for inciting racial hatred at his north London mosque and other terrorism-related charges.
Born in Egypt in 1958, he traveled to Britain to study before gaining citizenship through marriage in the 1980s.
A one-time nightclub bouncer in London's Soho district, al-Masri -- also known as Mustafa Kamal Mustafa -- has said he lost both hands and one eye while fighting against the Soviet occupation of Afghanistan. He often wore a hook in place of one hand.
In 1997, al-Masri became the imam of a north London mosque, where his hate-filled speeches attacking the West began to attract national attention and followers, including Richard Reid, the so-called "shoe bomber" who attempted to blow up a Miami-bound passenger airplane three months after the September 11, 2001, terrorist attacks.
Al-Masri has called the 9/11 attacks on the World Trade Center "a towering day in history" and described bin Laden as "a good guy and a hero."
He also described the Columbia space shuttle disaster in 2003 as "punishment from Allah" because the astronauts were Christian, Hindu and Jewish.
Al-Masri faces 11 charges in U.S. courts.
"As in the UK, legal counsel will be provided at the expense of the U.S. government if the defendants do not have the resources to pay themselves," a U.S. Embassy briefing note on the extradition said.
"The U.S.-UK Extradition Treaty also forbids use of the death penalty for anyone extradited from the UK."