Iran said earlier this month it was charging Shane Bauer, 27, Sarah Shourd, 31, and Josh Fattal, 27, with espionage. Their families say they strayed into Iran from northern Iraq accidentally while hiking at the end of July.
"Sarah, Shane and Josh are being well treated and seem to be physically well, but we are more and more worried about their state of mind," Nora Shourd, the mother of Sarah Shourd, said in a statement issued by the families.
"Our children are virtually cut off from the world outside their jail cells and have hardly any contact with each other. Not being able to call us, and not knowing their fate, must weigh on them ever more heavily as their detention drags on."
"It's high time Iran put an end to this, showed compassion and let them come home," said Cindy Hickey, Shane Bauer's mother.
U.S. Secretary of State Hillary Clinton and other U.S. officials have said Washington believes strongly that there is no evidence to support espionage charges against the three and urged Tehran to release them.
Iranian President Mahmud Ahmadinejad suggested in an interview with the U.S. television network NBC in September that the Americans' release might be linked to the release of Iranian diplomats he said were being held by U.S. troops in Iraq.
Under Iran's Islamic Shari'a law, espionage is punishable by death.
The families have set up a website to support their children, www.freethehikers.org, and urged friends and supporters of to send them messages through a special post office box where messages can be sent for delivery to Evin Prison in Tehran.
"It's vital for them to know they're getting support and one way to do that is to send them messages. It also shows the Iranian authorities that people care and won't let them be forgotten," said Laura Fattal, mother of Josh Fattal.