Mr Foley went missing in Syria in November 2012.
"We have never been prouder of our son Jim. He gave his life trying to expose the world to the suffering of the Syrian people." - Diane Foley
His mother Diane Foley released a statement earlier this week describing him as "an extraordinary son, brother, journalist and person."
She said: "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.
"We have never been prouder of our son Jim. He gave his life trying to expose the world to the suffering of the Syrian people."
The vast majority of media outlets have not broadcast the video, and people are being encouraged not to share it via social media.
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