The U.S. Attorney's Office in Chicago says Timothy Holmes, 31, publicly posted the threat on X on March 3.
It was made in reply to a post from the Israeli government's account.
The feds say their investigation revealed additional threatening communications.
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Holmes was arrested last Wednesday in Florida, and was ordered released on a $100,000 bond.
He's been charged with making a threat in interstate commerce to injure a person.
Holmes is not allowed to possess a firearm or dangerous weapon, contact victims or witnesses in the case or access social media or chat-based platforms.
He also must allow the U.S. District Court to install GPS monitoring and access his electronic devices to confirm compliance with the conditions and limit his travel to the Northern District of Illinois and the Middle District of Florida.
Holmes will appear in federal court in Chicago, but the date has not yet been set.