Bauer and Fattal pleaded not guilty Sunday at the five-hour hearing, which was closed to the public and media. A third American, Sarah Shourd, was released last September and pleaded not guilty in absentia.
"Now that the Court has heard their testimony firsthand, we hope and pray that truth and justice will at long last prevail," the Bauer and Fattal families said in a statement.
Bauer's mother and Fattal's mother and brother did not immediately return phone calls seeking further comment. Shourd did not immediately respond to an e-mail seeking comment.
Masoud Shafiei, the attorney for the Americans, said the judge decided there would be at least one more session in Tehran Revolutionary Court. The families said Shafiei told them he was not allowed to meet with Bauer and Fattal immediately before or after the hearing, but that he sat next to them in court and they appeared to be in good health. Shafiei's access to the men has been limited all along.
The three Americans were hiking in northern Iraq near the Iranian border in July 2009 when Iranian forces took them into custody. Iranian officials have accused them of spying for the U.S. but the Americans and their families insist it was an innocent hike and that the espionage charges are untrue. They have been held for 18 months.
Mohsen Milani, chairman of the Department of Government and International Affairs at the University of South Florida and an expert on Iranian politics, said any action in the case is a good sign.
"They are moving, which is positive for the accused," said Milani, a native of Iran.
He said the closed hearing was also a cause for hope.
"It gives greater room for the judiciary to do as it wishes," he said. "You could say they have left themselves wiggle room in terms of bringing the case to resolution on a quick basis."
The hikers' case has highlighted ongoing tensions between the U.S. and Iranian governments over the Middle Eastern country's nuclear program. Iranian President Mahmoud Ahmadinejad has asked for leniency for the Americans, but also has linked their plight to those of Iranian prisoners in the U.S., raising the possibility that Tehran wants to use the detainees as bargaining chips with Washington.
State Department spokesman P.J. Crowley said at a press briefing Monday that the department is aware the trial is proceeding and that Sunday's appearance ended in a continuance.
"We continue to call on the government of Iran to release the two hikers," Crowley said. "They have been in custody for far too long."
Crowley said Swiss diplomats in Iran, who represent U.S. interests in the absence of an official relationship between Washington and Tehran, are trying to find out exactly where the case is at after Sunday's hearing.
Shourd, who is Bauer's fiancée, was released on $500,000 bail arranged through the Gulf nation of Oman, which has close ties to the West and Iran. Iranian officials ordered Shourd back for the trial but she did not respond to the request, meaning the bail will likely be forfeited.
Shourd and Bauer had been living together in Damascus, Syria, where Bauer was working as a freelance journalist and Shourd as an English teacher. Fattal, an environmental activist, went to visit them in July 2009 shortly before their trip to northern Iraq.
Shafiei had hoped Sunday's hearing might bring resolution to the case. He said afterward he hoped the follow-up court date would be scheduled soon.
It's difficult to venture what kind of punishment Bauer and Fattal could face if found guilty because of the secretive nature of the Iranian judicial system. Their case recalls that of American-Iranian journalist Roxanna Saberi, who was arrested in Iran in January 2009, convicted of espionage and sentenced to eight years in prison. She was freed on appeal in May 2009.
Associated Press writer Matthew Lee in Washington contributed to this report.