The mission that rescued an American citizen "was characteristic of the extraordinary courage, skill and patriotism that our troops" show every day, Obama said.
"Tragically, we lost one of our special operators in this effort. Our thoughts and prayers go out to his family, just as we must always honour our troops and military families," he said in a statement.
The US Special Forces killed seven Taliban terrorists in the pre-dawn raid on Sunday carried out to rescue hostage Dr Dilip Joseph who was in "imminent danger of injury or death", NATO's International Security Assistance Force said on Sunday.
He had been abducted on December 5 by Taliban militants in the Surobi district of Kabul province.
Defence Secretary Panetta also commended the US Special Operations team who rescued American citizen captured by the Taliban in Afghanistan.
"I was deeply saddened to learn that a US service member was killed in the operation, and I also want to extend my condolences to his family, teammates and friends. The special operators who conducted this raid knew they were putting their lives on the line to free a fellow American from the enemy's grip," Panetta said in a separate statement.
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