The agency said someone speaking in bad Turkish, claiming to be phoning from abroad on behalf of the Lebanon Freedom Fighters group, called three times saying the group held U.S. Air Force Lieutenant Colonel Mike Couillard, 37, and his son Matthew, 10.
The two have been missing for three days in western Turkey after disappearing on a skiing trip. U.S. troops on Tuesday joined the search for them.
The caller said the pair would be killed within 48 hours unless the man it identified in Turkish as "Haci Ali Dirani" was freed, the agency said.
Israel has been holding Mustapha al-Dirani, better known as Abu Ali, since May last year. Dirani is leader of the Faithful Resistance anti-Israeli guerrilla group allied with pro-Iranian Hezbollah (Party of God) group.
A U.S. Embassy spokeswoman in Ankara said she was following up tips from Anatolian and private Show TV television channel reporting phone calls from the group. But no one from the group had called the embassy, she said.
A representative of Show TV said he had received one call in broken Turkish, possibly with an Arabic accent, threatening the life of the missing Americans.
"I asked them how I could believe them. They said, 'You'll see in 48 hours'," said Show TV Ankara representative Murat Yetkin.
Couillard and his son have been missing since Sunday, when they went on a day trip to Kartalkaya, a popular destination for Ankara skiers.
The officer was stationed in Ankara and embassy officials said he was assigned to a joint U.S.-Turkish military mission.
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