The Islamic State group beheaded four Iraqi Kurdish fighters following a joint raid with American special forces against the jihadists, according to a video posted online.
The US-Kurdish operation last week, which freed some 70 people from an IS prison, deepened American involvement in the war against the jihadists and led to the first US combat fatality in Iraq since its 2011 withdrawal from the country.
The video sought to portray the operation as a failure, with speakers saying the attacking forces were unable to overcome numerically inferior jihadists and displaying used first aid supplies that were left behind.
It included images of areas said to have been hit by air strikes in the course of the operation, and ended with the execution of four men, said to be members of the Kurdish peshmerga security forces.
Four black-clad masked militants used knives to behead the men, who were dressed in orange jumpsuits and had their hands bound behind their backs.
It was not clear when the beheadings took place.
IS has seized control of large parts of Iraq and Syria, declaring a cross-border "caliphate", imposing its brutal interpretation of Islam and committing widespread atrocities.
A US-led coalition launched air strikes against the jihadists in August 2014, supporting Iraqi forces, including Kurdish fighters, in attempts to retake lost ground.