In Washington, a U.S. military spokeswoman lent credibility to the claim, saying "initial reports indicate the crash may have been caused by hostile fire" in Kunar province, which borders Pakistan.
"The status of the service members is unknown at this time," she said.
Taliban spokesman Abdul Latif Hakimi said militants had shot down the aircraft in the village of Shorak using "a new type of weapon," which he did not describe. He also claimed to have videotape of the crash and its aftermath.
Meanwhile, the rescue operation has been complicated by the high altitude of the crash site, a remote, mountainous area west of the town of Asadabad, the BBC said.