A US journalist and a South African teacher held by al Qaeda militants in Yemen were killed alongside 10 of their captors during a rescue attempt by US and Yemeni forces, senior officials said on Saturday.

US 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," US 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.

Kerry and US Secretary of Defense Chuck Hagel both said the decision to mount the raid was based on fears that AQAP planned to kill Somers.

"Earlier this week, AQAP released a video announcing that Luke would be murdered within 72 hours. Along with other information, there was a compelling indication that Luke's life was in immediate danger," Kerry said.

U.S. officials on Thursday said American forces had already attempted to rescue Somers, without giving further details. Yemeni officials had previously disclosed the release of six Yemenis, a Saudi and an Ethiopian hostage in a raid on Nov 25.

AQAP on Thursday released a video showing a man it said was Somers speaking to the camera and saying: "I'm looking for any help that can get me out of this situation. I'm certain that my life is in danger".

Reuters was not able to independently verify the authenticity of that video, which was reported on by SITE Monitoring.

Yemen's Defence Ministry had earlier said that a military operation had succeeded in freeing a U.S. hostage as well as killing 10 members of the al Qaeda group holding him. But Major General Ali al-Ahmadi, chief of the national security bureau in Yemen, later confirmed he had died.

The operation involved an air strike followed by a raid by U.S. and Yemeni forces, a local security official said. It took place in the Wadi Abdan Al Daqqar region of Shabwa Province in southern Yemen and targeted an al Qaeda group headed by Mubarak al-Harad.

Al Qaeda and allied Islamist militants have a strong presence in large parts of southern and eastern Yemen, an impoverished Arabian Peninsula country where the government has little control outside main cities.-Reuters