Regrettably, Luke was not present, though hostages of other nationalities were present and were rescued," the National Security Council said.
A man identifying himself as Luke Somers, who was abducted in 2013, has appeared in a video, saying his life is in danger and appealing for help.
The video also shows a member of al-Qaeda in the Arab Peninsula (AQAP) threatening to kill Mr Somers unless unspecified demands are met.
Mr Somers, 33, worked as a journalist and photographer for local news organisations and his material appeared on international news outlets, including the BBC news website.
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Analysis by Aleem Maqbool, BBC News, Washington
The US saw an opportunity to rescue one of its civilians and took it. But the risk was that failure would put the hostage in further danger. In this video, al-Qaeda in the Arab Peninsula says this is exactly what has happened.
Scrutiny of US policy on dealing with kidnappers has increased with the deaths of three Americans held by Islamic State militants in Syria - each paraded on video, threatened and then beheaded.
The Obama administration has been criticised for not paying ransoms, not allowing hostage families to speak out and not taking opportunities to negotiate.
While the White House stands by its policies, the president has ordered a review.
With its videos and killings, Islamic State has achieved its objectives of spreading fear and gaining notoriety, and this new video from Yemen suggests its propaganda is inspiring other groups.
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'Classified'
On 25 November, US and Yemeni forces rescued six Yemenis, a Saudi and an Ethiopian being held by AQAP in an operation at a mountain cave in the remote Hajr al-Sayar district of Hadramawt province. Seven militants were reportedly killed.
US National Security Council spokeswoman Bernadette Meehan said: "As soon as the US government had reliable intelligence and an operational plan, the president authorised the department of defence to conduct an operation to recover Mr Somers."
A man identifying himself as Luke Somers, who was abducted in 2013, has appeared in a video, saying his life is in danger and appealing for help.
The video also shows a member of al-Qaeda in the Arab Peninsula (AQAP) threatening to kill Mr Somers unless unspecified demands are met.
Mr Somers, 33, worked as a journalist and photographer for local news organisations and his material appeared on international news outlets, including the BBC news website.
line
Analysis by Aleem Maqbool, BBC News, Washington
The US saw an opportunity to rescue one of its civilians and took it. But the risk was that failure would put the hostage in further danger. In this video, al-Qaeda in the Arab Peninsula says this is exactly what has happened.
Scrutiny of US policy on dealing with kidnappers has increased with the deaths of three Americans held by Islamic State militants in Syria - each paraded on video, threatened and then beheaded.
The Obama administration has been criticised for not paying ransoms, not allowing hostage families to speak out and not taking opportunities to negotiate.
While the White House stands by its policies, the president has ordered a review.
With its videos and killings, Islamic State has achieved its objectives of spreading fear and gaining notoriety, and this new video from Yemen suggests its propaganda is inspiring other groups.
line
'Classified'
On 25 November, US and Yemeni forces rescued six Yemenis, a Saudi and an Ethiopian being held by AQAP in an operation at a mountain cave in the remote Hajr al-Sayar district of Hadramawt province. Seven militants were reportedly killed.
US National Security Council spokeswoman Bernadette Meehan said: "As soon as the US government had reliable intelligence and an operational plan, the president authorised the department of defence to conduct an operation to recover Mr Somers."