The hackers, known as the United Cyber Caliphate (UCC), ordered those watching to, "Kill them wherever you find them", Fox News reported.
The video, just under six minutes, begins with a warning for the United States.
"We have a message to the people of the US and most importantly your President (Donald) Trump," the text on the screen reads.
In the posting on Telegram -- a private messaging app -- the group first warned that a release of the names was imminent.
"More than 7,000 of the names were from the US," a source from the cyber department at SITE was quoted as saying.
"Know that we continue to wage war against you. Know that your counter attacks only make us stronger. The UCC will start a new step in this war against you," the message was quoted as saying.
Terror analysts were quoted as saying that it is not yet determined how serious a threat the list may pose in the US and elsewhere.
The UCC released a video on March 16 saying its leader, Osed Agha, had been killed in a US airstrike. The video threatened retaliation for his death.
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