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MINNEAPOLIS (AP) — The mothers of three American hikers held in Iran on suspicion of espionage said Thursday they hope a report that their children were arrested on the Iraqi side of the border will help lead to their release.

Shane Bauer, Sarah Shourd and Josh Fattal were arrested July 31 during what their families have said was a simple hiking trip along the Iraq-Iran border. They have said if the hikers crossed into Iran it was an accident.

The Nation reported Thursday that two witnesses from a Kurdish village near the border say the Americans were on Iraqi territory when they were arrested by Iranian forces. The publication said the witnesses wouldn't allow their names to be used because they feared retaliation from Iran.

Two Iraqi security officials contradicted the account, telling The Associated Press that the hikers were arrested on Iranian soil.

"We have to focus and assimilate this, but it's shocking," Nora Shourd, Sarah's mother, said in an interview on CNN. "It's shocking it hasn't come out in the public, that it happened to these kids, and that this is the reason they're being held."

"What it does for me is it pushes me into the hope that the Iranian authorities can investigate this, see it for what it is, and release them immediately," Cindy Hickey, Shane Bauer's mother, said in an interview with AP.

Bauer had worked as a freelancer journalist, and wrote at least one piece on Iraq for The Nation, but the publication has said he wasn't on assignment for them at the time of his arrest.

The magazine said its story was based on a five-month investigation. It described its witnesses as people from Zalum, a few miles from the Iran border.

"Obviously these are disconcerting allegations," State Department spokesman Mark Toner said. "We have no evidence to back up those allegations. We would just again call on the Iranian authorities to immediately release Josh Fattal, Shane Bauer, Sarah Shourd as well as all other American citizens who are being unjustly detained."

The Nation's report said the witnesses followed the obviously Western hikers out of curiosity as they descended a mountain straddling the border. The witnesses said uniformed guards from Iran's national police force waved the hikers toward the Iranian side using threatening gestures and when their calls were ignored, one officer fired a round in the air. The hikers continued to hesitate, and the guards walked a few yards into Iraqi territory to arrest them, the witnesses said, according to The Nation.

The rugged, mountainous region is part of the disputed area between Iraq and Iran, with few fences or distinct border markings, making it difficult for visitors to know which side they are on. It's also seen sporadic clashes in recent years between Iranian forces and a Kurdish rebel group known as the Party for Free Life in Kurdistan.

Iraqi border police Brig. Gen. Ahmed Gharib told AP Thursday that the three Americans passed through Zalum, a tourist village near the border where there is a waterfall and a cafe, on the way to climbing a mountain — the peak of which he said is in Iran.

"The three Americans were arrested inside Iranian territory," said Gharib, who is based in the Kurdish-Iraqi city of Sulaimaniyah.

"When they reached the top of mountain, the Iranian guards arrested them because there is an Iranian outpost on the top of mountain," he said.

Hakim Qadir Hama, the director of the Sulaimaniyah provincial security service, told AP that Zalum village police warned the Americans about climbing the mountain as they would all but certainly stray across the Iranian border, "but no one listened to them." Hama said authorities launched an investigation the day after the hikers disappeared, and ultimately concluded that the Americans had entered Iran and were arrested there.

Laura Fattal, Josh's mother, said she was grateful that the magazine's report had put the hikers back in the news.

"If this helps gain their release, it's wonderful," she said.

The hikers' mothers have grown increasingly frustrated since traveling to Iran in May to visit their children, who were being held at Evin Prison in Tehran. Earlier this month, they demanded that Iran release the hikers or put them on trial, and said they were being used as pawns in a standoff with the U.S.

Iran's top human rights official said recently that the three would probably go on trial soon if prosecutors decide they have enough evidence.

Fattal, 28, is from Pennsylvania. Shourd, 31, is from California and Bauer, 27, from Minnesota. All three are graduates of the University of California at Berkeley.

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Associated Press writers Matthew Lee in Washington, Yahya Barzanji in Sulaimaniyah, Iraq, and Lara Jakes in Baghdad contributed to this report.