Prosecutors have charged the cleric, Abu Qatada, with conspiring to carry out terrorist attacks against Israelis, Americans and other Westerners in Jordan in two foiled plots in 1999 and 2000.
The 53-year-old militant preacher was deported from Britain to Jordan yesterday.
Abu Qatada's lawyer, Tayseer Thiab, says he submitted a formal bail request for his client today.
A military prosecutor says the State Security Court will respond "within 48 hours."
Suspects accused of serious crimes such as terrorism are rarely granted bail in Jordan.