Al-Qaeda has blamed US President Barack Obama for the deaths of two hostages - an American photojournalist and a South African teacher - during a failed rescue attempt by US troops over the weekend.
Luke Somers and South African national Pierre Korkie were killed by their captors on Saturday when US and Yemeni troops stormed an al-Qaeda base in southwestern Yemen.
"Obama made the wrong decision, and signed the death warrant for his American compatriot [Somers]", Al-Qaeda in the Arabian Peninsula (AQAP) official Nasser bin Ali al-Ansi said in the video released on Thursday.
The failed US raid came just a day before Korkie was due to be released under a deal with the kidnappers.
US Defence Secretary Chuck Hagel said there were "compelling reasons" to believe Somers' life was in danger before the rescue operation was launched.
The New York Times said Somers was shot by his captors as the joint raid by US and Yemeni forces unfolded and was badly wounded when the commandos reached him. He died while being flown to a US naval base in the region, the paper reported.
Somers was seized in the Yemeni capital in September 2013 while he worked as a photojournalist for the Yemen Times. Korkie was abducted together with his wife in May 2013, but she was released in January.
Somers was also a contributor to Al Jazeera.
AQAP, considered by Washington as the most dangerous affiliate of Al-Qaeda, has exploited instability in the impoverished country since a 2011 uprising forced president Ali Abdullah Saleh to step down.
And in recent years the group has carried out a growing number of abductions, with several hostages still in captivity.