Facebook founder Mark Zuckerberg and Twitter CEO Jack Dorsey are the latest high-profile individuals targeted by ISIS.
A 25-minute propaganda film, "Flames of the Supporters," was released by a group calling itself "the sons of the Caliphate army." They threaten to delete both Facebook and Twitter and the video shows photographs of both tech giants being targeted by bullets.
It comes after both social networks deactivated accounts suspected of spreading terrorism.
The video warns: "You are not in our league. If you close one account we will take 10 in return and soon your names will be erased after we delete your sites, Allah willing."
The video also shows hackers altering existing Facebook and Twitter accounts and posting Islamic State propaganda. ISIS alleges it has hacked more than 10,000 Facebook accounts and more than 5,000 Twitter profiles.
“Many of these accounts have been given to supporters,” the video said.
Facebook and Twitter have not responded to the threat.