GlobalPost, one of the news services for which Foley worked, Thursday published the message, which was received August 12.
"You and your citizens will pay the price of your bombings! The first of which being the blood of the American citizen, James Foley!", it said.
In the email, published with the family's consent, the IS said the journalist would be "executed as a direct result of your transgressions towards us!", referring to the recent intervention in Iraq, where the US has carried out airstrikes on IS positions in the north for more than a week.
In an article accompanying the message, the GlobalPost denied claims by the IS that they had given the family "many chances to negotiate" the journalist's release.
IS Mail: You and your citizens will pay the price of your bombings
Foley was kidnapped in November 2012 and his family had no news of him until Nov 26, 2013, when it received a message asking for $132 million and the release of several prisoners in the US in exchange for his freedom.
The last and final message to the family was sent Aug 12, only a week before the news of Foley's death Aug 19.
Foley was kidnapped on his way to the Turkish border, and at first was thought to have been captured by pro-government militias.
In the video of Foley's decapitation released last Tuesday, the journalist bade farewell to his family and accused the US government of being responsible for his execution due to its recent intervention in Iraq.
Another kidnapped US journalist, Steven Joel Sotloff, also appears in the video with a warning that his life "depends on (US President Barack) Obama's next move".
The US has continued bombing positions of the IS in northern Iraq with fresh air attacks close to the strategic Mosul Dam, as part of a campaign to help Iraqi troops combat IS.