"The health of Abu Anas al-Libi has deteriorated because of a hunger strike,"Abdullah al-Raghie told AFP ahead of his second appearance in court on Tuesday.
"His state of health has become more serious," he said, citing a defence attorney.
Raghie said his father was suffering from hepatitis C, an infection of the liver, and added Libyan authorities, who have protested to the United States over his October 5 capture, had pledged to form a defence team.
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On October 15, Libi, 49, pleaded not guilty in court to conspiracy charges over the 1998 US embassy bombings in East Africa that killed 244 people.
The prosecution said Libi, whose given name is Nazih Abdul Hamed al-Raghie, was a clear danger to the public and a flight risk with no family in the United States.
The judge ordered him detained and adjourned the next hearing until October 22.
Before his arrival in New York, Libi was interrogated on the USS San Antonio, a US amphibious transport ship that had been operating off Libya in the Mediterranean.
But US television network CBS said his questioning was cut short after he started to refuse food and water.