In the 25-minute video, the IS claim they are fighting back against efforts by the social media giants to wipe their platforms of accounts promoting terrorism.
Read more from our special coverage on "ISIS"
The video includes a direct threat to the tech entrepreneurs, branding them allies of the American "Crusader government".
Pictures of Zuckerberg and Dorsey can be seen being blasted with a hail of bullets in the amateur footage which emerged.
The video, titled "Flames of the Supporters" and released by a group calling themselves "the sons of the Caliphate army", ends with a direct threat to the two men, The Sun reported.
A slide toward the end of the video reads, in English: "To Mark and Jack, founders of Twitter and Facebook and to their Crusader government. You announce daily that you suspended many of our accounts and to you we say: is that all you can do? 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 you (sic) sites, #Sons_Caliphate_Army".
In a separate slide, they also claim to have hacked more than 10,000 Facebook accounts, 150 Facebook groups, and more than 5,000 Twitter accounts.
Two scholars who track ISIS activity online confirmed that the video was posted to multiple ISIS forums, including some on the social media platform.
ISIS and related terrorist groups have targeted Dorsey at least twice in the past year. A group of self-identified ISIS supporters threatened the Twitter founder and CEO in March of 2015 for closing hundreds of their social media accounts.
In its threat, the group claimed that Dorsey and his company started a "war" against the Islamic State, and that the "necks" of Twitter employees have "become an official target to ISIS soldiers and supporters."
Twitter seems to have only stepped up its efforts to wipe ISIS off its platform since then.
A few weeks ago, the company announced it had suspended more than 125,000 accounts for threatening or supporting terrorist acts over the past several months.
Twitter also said it has grown its team that looks into reports of terror activity on its network.
Zuckerberg reiterated his stance and Facebook's policy on helping to fight terrorism online.
A Facebook spokeswoman did not immediately respond to request for comment on this week's threat.
A Twitter spokesman reiterated the company's policy and progress on suspending accounts that promote terrorism or any violent threat.
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