The man, Adam Bies, 46, compared federal agents to K.G.B. and Nazi officers and threatened to kill them, prosecutors said in a complaint. Mr. Bies posted the messages on Gab, the far-right social media app, and wrote under the pseudonym Adam Kenneth Campbell. He explained in a chat log obtained by investigators that he used the false name “so that corporate Murica’” could not “Google” him “out of a job.”

In one of the messages, posted on Aug. 10, two days after the search of Mr. Trump’s club, Mar-a-Lago, Mr. Bies wrote of the F.B.I., “You’ve declared war on us and now it’s open season on YOU,” according to the complaint.

The next day, he posted a message reading, “I sincerely believe that if you work for the F.B.I., then you deserve to die.” On Aug. 12, he invited the “feds” to come get him. Prosecutors said most of the threats posted were made in the days after the F.B.I. executed a search warrant to retrieve classified documents from Mr. Trump’s home.