Foley's mother, Diane Foley, released a statement through a Twitter accountthe family had used to campaign in which she confirmed his death and said he died "trying to expose the world to the suffering" of the Syrian people.
"We implore the kidnappers to spare the lives of the remaining hostages. Like Jim, they are innocents. They have no control over American government policy in Iraq, Syria or anywhere in the world," the statement read."We thank Jim for all the joy he gave us. He was an extraordinary son, brother, journalist and person. Please respect our privacy in the days ahead as we mourn and cherish Jim."
The group claimed in the video to be holding another US journalist and said his life depended on US President Barack Obama's next move.
"The life of this American citizen, Obama, depends on your next decision," said a masked man in the video posted on social media sites, speaking English with a British accent as he held a prisoner the video named as Steven Sotloff.
The video could not immediately be verified.
Foley, 41, was contributing videos to the AFP news agency for the media company GlobalPost before he was kidnapped on November 22, 2012 by unidentified gunmen.
"We have seen a video that purports to be the murder of US citizen James Foley by ISIL. The intelligence community is working as quickly as possible to determine its authenticity," Caitlin Hayden, a spokesperson for the US National Security Council, said on Wednesday.