(CNN) -- The mothers of three American hikers detained in Iran have sent an open letter to Iran's justice minister, appealing for their children's freedom as the one-year anniversary of their detention approaches.
"The Islamic Republic of Iran has held our children Shane Bauer, Sarah Shourd and Josh Fattal in virtual isolation from their families and the world for almost 12 months," said the letter, dated Wednesday and addressed to Ayatollah Sadegh Larijani. "We call on you to end their unjust and arbitrary detention before the one-year anniversary of their arrest on July 31."
The three hikers were detained after they allegedly strayed across an unmarked border into Iran while hiking in Iraq's Kurdistan region. However, The Nation magazine reported last month that two witnesses have said they saw members of Iran's national police force cross into Iraq to apprehend the three.
Tehran has claimed the three hikers are spies. Iran's intelligence minister has hinted the country may consider releasing them in exchange for the release of Iranian prisoners, according to state media.
The hikers' mothers visited them earlier this year. "We were grateful for the opportunity to visit our children in Tehran in May, but nothing has happened since then," said the Wednesday letter, signed by Cindy Hickey, Nora Shourd and Laura Fattal.
They said the lawyer representing their children, who are held in Tehran's Evin Prison, is continually denied access to them "in violation of all due process." The three, ages 27 to 31, have been able to call their families just once, and not at all since the May visit, the letter said.
"Our children's imprisonment in the absence of any certainty as to their fate or to the specific allegations against them is unlawful and inhumane," the letter said.
"We demand an immediate end to Sarah's solitary confinement and immediate access to the results of her medical tests. Sarah has serious health problems and her continued isolation will do lasting damage to her mental and physical well-being."
"... We urge the Iranian authorities to live by the principles of compassion that we so admired in the Iranian people during our visit," the mothers wrote. "It surely does Iran no good in the eyes of the world to continue to deprive our children of their liberty."
Bauer and Shourd got engaged in prison and plan to get married after their release, their mothers have said.