The Islamist group released a video showing a masked militant purportedly beheading the reporter, who has been missing since he was seized by armed men in Syria in November 2012.
"Find James Foley," the campaign run by his family to secure the 40-year-old freelancer's release, posted a public message online following the release of the video asking for time "to seek answers."
Foley was an experienced correspondent who had covered the war in Libya before heading to Syria to follow the revolt against Bashar al-Assad's regime for the Global Post, AFP and other outlets.
According to witnesses, Foley was seized in the northern Syrian province of Idlib on November 22, 2012. His family has not heard from him since, despite a public campaign for information.
In the five-minute video, distributed online by known Islamic State sources, the group declares that Foley was killed after US President Barack Obama ordered air strikes against IS positions in northern Iraq.
The purported execution is carried out in an open desert area with no immediate signs as to whether it is in Iraq or Syria, by a black-clad masked militant who speaks in English with a British accent.