NATO said it is investigating the cause of the crash. The coalition had no immediate comment on the insurgents' claim that they shot down the helicopter.
Officials in Kandahar province said the helicopter went down in the north of the province. Kandahar is a traditional Taliban stronghold and the spiritual birthplace of the hardline Islamist movement that ruled Afghanistan before being ousted in 2001 by the U.S.-led alliance for sheltering al-Qaida's terrorist leaders.
Among the dead were seven American service members, three members of Afghan security forces and one Afghan civilian interpreter, said Jamie Graybeal, a spokesman for the coalition.
He said the aircraft was a UH-60 Black Hawk but declined to give any details of the aircraft's mission
Taliban spokesman Qari Yousef Ahmadi said insurgent fighters shot down the helicopter in Kandahar province on Thursday morning.
"Nobody survived this," Ahmadi told The Associated Press by phone.
The helicopter went down in Kandahar's Shah Wali Kot district, which lies in the northern part of the province, a spokesman for the provincial government said.
"We don't know if it was shot down by the Taliban, or if it had mechanical problems," said the spokesman, Ahmad Jawed Faisal.
Thursday's crash is the deadliest since a Turkish helicopter crashed into a house near the Afghan capital, Kabul, on March 16, killing 12 Turkish soldiers on board and four Afghan civilians on the ground, officials said.
In August last year, insurgents shot down a Chinook helicopter, killing 30 American troops, mostly elite Navy SEALs, in Afghanistan's central Wardak province.
At least 221 American service members have been killed in Afghanistan so far this year.
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Associated Press writers Mirwais Khan in Kandahar, Afghanistan, and Amir Shah and Deb Riechmann in Kabul contributed to this report.
