Abedini's lawyer indicated that neither she nor the Christian pastor expected to be allowed to attend Tuesday's hearing after Abedini provided an Iranian judge a written statement and answered prosecutors' questions Monday, CNN reported.
Last summer, Abedini, who has been arrested several times before in Iran, was on a bus crossing from Turkey into Iran when immigration officials seized his passport. He was placed under house arrest and in September he was jailed in Evin prison while he awaited trial.
Abedini and his wife live in Idaho but his parents still live in the Islamic republic.
Tiffany Barrans, one of Abedini's attorneys and legal director for the American Center for Law and Justice, said the church leaders in Iran face either trying to avoid being called as witnesses or testify and possibly face similar charges.
"They are all very fearful to have to show up," she told CNN on a conference call with the minister's wife, Nahgmeh Abedini, and Jordan Sekulow, the center's executive director. The center provides legal counsel and takes legal action involving freedom and liberty issues around the world.
Monday, the Iranian state-run media reported Abedini would be released on bail soon, but his wife told CNN the court has rejected the family's attempt to pay.
His wife and lawyers said bail was set at $116,000 but the court rejected it on a technicality.
"His family [in Iran] has been running in circles to pay his bail, and each time the court has rejected them and ask for more documents," she said. "For us, it's like they are crying wolf."