He was originally arrested in part of a sweep against al-Qaeda and was charged with being a member of the group, other officials said.
Rich Wolf, a US Federal Buerau of Investigation (FBI) spokesman, said that the agency was looking into the case.
Charles Mobley, the suspect's father, said on Friday morning: "I can tell you this: He's no terrorist."
His mother told local media that she spoke to her son in January when he was in Yemen and that the FBI had previously visited her home.
Other people have commented that Mobley showed strong religious views in high school.
Roman Castro, who went to school with Mobley and subsequently did a tour with the US Army in Iraq, said when he last saw him about four years ago, Mobley yelled: "Get the hell away from me, you Muslim killer!"
Mobley moved to Yeman about two years ago to study Arabic and Islam, a former neighbour said.
He had previously been a member of his school wrestling team and was a karate black-belt.