Tehran, Iran (CNN) -- The families of American hikers charged with espionage in Iran are pleased that the hikers "had the opportunity to explain their innocence to the court," according to a joint news release Monday.
The families of Shane Bauer and Josh Fattal said they "hope that the Iranian authorities will now move to resolve their case so that they finally can come home after 18 months of detention, isolation and uncertainty."
The trial began Sunday in Iran. The proceedings were closed to the public but, the families said, "we understand that Shane and Josh were able to make lengthy statements about their innocence both verbally and in writing."
The trial is expected to resume in the next few weeks, according to the office of the lawyer representing them and a diplomatic official.
The lawyer, Masoud Shafii, said Monday the next session could be within a week or two, although he wasn't certain of the timing.
The Swiss ambassador to Iran, who represents American interests in the country, told CNN on Sunday that the trial will likely continue in the near future.
"It's going to be soon," Ambassador Livia Leu Agosti said, though she declined to divulge her source. "It's not going to be another three-month wait."
Iran accuses Americans Shane Bauer, 28, Josh Fattal, 28, and Sarah Shourd, 32, of spying and trespassing.
They were detained July 31, 2009, after they allegedly strayed across an unmarked border into Iran while hiking in Iraq's Kurdistan region.
Shourd was released on bail in September 2010 because of a medical condition and immediately left the country. She has not responded to a court summons to return to stand trial, Shafii said Saturday.
Iranian authorities said she will be tried in absentia if she doesn't appear in court.
The trial is closed to the press and the public, as is normally the case with revolutionary court proceedings. The hikers pleaded not guilty, Shafii said.
Shafii said he had been denied permission to see Bauer and Fattal the day before the trial began. He told CNN he has reviewed his clients' case file and doesn't see any evidence of a crime, and has requested permission to meet with his clients soon.
"In my opinion, they haven't done anything wrong," Shafii said. "The accusation of spying is baseless, and if they trespassed into Iran, it wasn't their fault."
Shafii said the border area where the hikers are accused of trespassing is unmarked and anyone could unwittingly cross over into Iran.
"I can honestly say they were doing very well. They were wearing normal clothes, not prison uniforms," Shafii said after seeing the hikers in court on Sunday. "They didn't have handcuffs on but naturally they were escorted by security."
Human rights groups have condemned their arrests and their lengthy wait for a trial in Tehran's notorious Evin prison.
But Tehran's prosecutor general defended the delay.
"Crimes related to espionage are serious which are dealt with in all countries," Abbas Jafari-Dolatabadi, Tehran's prosecutor general, told state-run Press TV. "The prosecutor must investigate accurately."
CNN's Shirzad Bozorgmehr and Reza Sayah contributed to this report