Hamza was convicted in a British court in 2006 of inciting hatred and is serving a 7-year prison sentence. British Prime Minister Gordon Brown wanted the cleric extradited to the United States before his prison term was finished.
The European court called on the British government and Hamza's lawyers to issue a brief regarding the treatment the cleric could face in the U.S. prison system were he to stand trial there, London's Guardian newspaper reports.
"The issue the court wants to decide is whether the conditions in the U.S. prisons are so draconian it amounts to inhumane conditions," the newspaper quoted his lawyer Muddassar Arani as saying.
Washington accuses Hamza of playing a role in the kidnapping of 16 tourists in Yemen in 1998. Three British civilians were killed in the hostage-taking. Washington claims he has ties to al-Qaida and the Taliban and allegedly established a terrorist training camp in Oregon in 1999.
His lawyer said the European court gave London until September to issue a new submission on human rights clams.