U.S. Secretary of State John Kerry said al Qaeda militants killed Luke Somers, 33, and another foreign national hostage during the rescue operation, which he said was only approved because of information that their lives were at imminent risk.
Al Qaeda in the Arabian Peninsula (AQAP) is seen by Washington as one of the movement's most dangerous branches, and it has worked with the Yemeni government and via drone strikes to attack its leadership in southern and eastern parts of Yemen.
"The callous disregard for Luke's life is more proof of the depths of AQAP's depravity, and further reason why the world must never cease in seeking to defeat their evil ideology," U.S. President Barack Obama said in a statement.
He said he had authorised the attempted rescue and said the United States would "spare no effort to use all of its military, intelligence and diplomatic capabilities to bring Americans home safely, wherever they are located".
Somers was moved from the scene of the rescue attempt but died later from his wounds, a senior official in the Yemeni president's office said.
Relief group Gift of the Givers said South African teacher Pierre Korkie was killed in the operation.
"We received with sadness the news that Pierre was killed in an attempt by American Special Forces, in the early hours of this morning, to free hostages in Yemen," it said in a statement on its website.
However, there was no new information about three other hostages, a Briton, a Turk and a Yemeni, who had previously been held alongside Somers and Korkie, a Yemeni security official told Reuters.
Lucy Somers, the photojournalist’s sister, told the Associated Press that she and her father learned of her brother's death from FBI agents at 0500 GMT (12 a.m. EST) Saturday.
"We ask that all of Luke's family members be allowed to mourn in peace," she said from London.

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