The hackers are known as the United Cyber Caliphate (UCC).
In a posting Sunday night on Telegram, a private messaging app, the group first warned that a release of the names was imminent.
A short time later, the hackers posted the actual list.
"More than 7,000 of the names were from the U.S.," a source from the cyber department at SITE Intelligence Group told Fox News on Wednesday.
A six minute video was posted, beginning with a warning for the US.
"We have a message to the people of the U.S. and most importantly your President Trump," the text on the screen reads.
"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 said.
SITE is currently working to determine the primary source of the list, which includes individual phone numbers and emails.
"We're trying to determine where the list came from and also identify a common theme among all the inviduals," the source said.
Terror analysts say it's not yet determined how serious a threat the list may pose in the U.S. and elsewhere.
"This group has released several 'kill lists' in the past and so far there's been no confirmed incident of someone on the list being directly targeted or attacked," the source said.
The UCC released a video on March 16 saying its leader, Osed Agha, had been killed in a U.S. airstrike. The video threatened retaliation for his death.