The three Americans – Shane Bauer, Sarah Shourd and Josh Fattal – have now been missing for 12 days.
"As loving parents, nothing causes us more heartache than not knowing how our children are, and not being able to talk to them and learn when we will hold them in our arms again," the families write in the statement.
"Shane, Sarah and Josh are young travelers who share a great love of the world and a deep respect for different cultures, societies and religions," they write. "We believe that when the Iranian authorities speak to our children, they will realize that Shane, Sarah and Josh had no intention of entering Iran and will allow them to leave the country and reunite with their families."
"We continue to hope that this misunderstanding will be resolved as quickly as possible," they add.
Bauer is a 27-year-old freelance journalist who has been living in Damascus, Syria with the 31-year-old Shourd, an English teacher who has been preparing for graduate school. Fattal, 27, is an environmentalist who teaches sustainable living skills in Oregon. (Pictured above: Dukan Resort near Sulaimaniyah, where the three hikers were last seen.)
A fourth member of their party, Shon Meckfessel, stayed behind at the hotel because of a cold and was not on the hiking trip. He released a statement last week explaining that the hikers' entry into Iran had been a mistake.
Iran reportedly formally notified the U.S. State Department that it has the hikers in detention today. Swiss officials have stepped in to represent American diplomatic interests in the matter.