Three American hikers detained in Iran since July 31 entered the country by mistake and their families are hoping for a quick resolution that will reunite them with their children, the families said in a statement Tuesday.

Joshua Fattal, freelance journalist Shane Bauer and Bauer's girlfriend, Sarah Shourd, were hiking near a waterfall on a mountain in Iraq's self-ruled Kurdish region on July 31 when they accidentally crossed the border into Iran, according to family members.

They contacted a colleague to say they had entered Iran by mistake and were surrounded by troops, according to a Kurdish official in Iraq. Iran's state television said the Americans were arrested after they did not heed warnings from Iranian border guards.

"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," the families said in a statement to The Associated Press. "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."

The families said all three are graduates of the University of California, Berkeley.

Bauer, 27, and Shourd, 31, previously lived in the San Francisco Bay area, but the statement said they most recently had been living in Damascus, Syria. Pacific News Service had hired Bauer to cover the elections in northern Iraq's self-ruled Kurdish region; Shourd has written for a number of online publications, including Brave New Traveler.

Fattal, 27, spent three years recently living with a group dedicated to sustainable farming near Cottage Grove, Oregon. He lived with about nine others and worked as the group's intern coordinator before leaving about eight months ago.

Bauer's mother, Cindy Hickey, of Pine City, Minnesota, and Shourd's mother, Nora Shourd, of Oakland, California, said last week that they hoped the three would be allowed to safely leave Iran. Fattal's father, Jacob, who runs a tech magazine outside Philadelphia, echoed those sentiments.

From January to June, Fattal traveled overseas as a teaching assistant with the International Honors Program, visiting Switzerland, India, South Africa and China on a global ecology program. Fattal had been a student in the program during college.

A fourth person, Shon Meckfessel, was supposed to have gone on the hike but did not because he felt sick.