According to Yemen’s defence ministry, Al-Qaeda moved hostages, including the US journalist, a Briton and a South African, days before that US-Yemeni raid in southeastern Hadramawt province.
The whereabouts of the Briton are unknown.
Yemeni officials said eight other hostages were freed in the earlier operation.
Yemen is a key US ally in the fight against Al-Qaeda, allowing Washington to conduct a long-standing drone war against the group on its territory.
AQAP is considered by Washington to be the most dangerous affiliate of Al-Qaeda.
The execution threat by AQAP followed the murder of five Western hostages since August by the Islamic State group that controls parts of Syria and Iraq.
Two US journalists, James Foley and Steven Sotloff, American aid worker Peter Kassig and British aid workers Alan Henning and David Haines were all beheaded.
Al-Qaeda has exploited instability in impoverished Yemen since a 2011 uprising forced president Ali Abdullah Saleh to step down.
In recent years there has been a growing number of abductions in Yemen by Al-Qaeda.
The militants remain active in southern and eastern regions of Yemen despite several military campaigns by government forces.
Al-Qaeda militants have allied with Sunni tribesmen in southern Yemen to halt the advance of Shiite Huthi militias who seized Sanaa in September unopposed, and who have since extended their control to coastal areas and regions south of the capital.