The San Antonio Express-News reports both were arrested Dec. 16 in an undercover investigation and remain in custody. A bond hearing Thursday in San Antonio for Coronel was canceled after he was indicted.
Coronel served at Ministerios Epicentro Donde Nace La Bendicion in Austin. He's also charged with making a false statement to immigration officers.
A woman who answered a phone number listed for Coronel's church declined comment.
Tovar, who's accused of being in the U.S. illegally, is held without bond.
