WASHINGTON — Federal prosecutors have charged a former F.B.I. agent with illegally entering the Capitol during the Jan. 6 riot and said he had called police officers Nazis as he encouraged a mob of Trump loyalists to kill them.

The former agent, Jared L. Wise, was arrested on Monday and faces four misdemeanor counts, including disrupting the orderly conduct of government and trespassing, after agents received a tip in January 2022 that he had been inside the Capitol, according to a criminal complaint.

Mr. Wise, 50, told the police they were like the Gestapo, Nazi Germany’s feared secret police, the complaint said. When violence erupted, he shouted in the direction of rioters attacking the law enforcement officers, “Kill ’em! Kill ’em! Kill ’em!”

Mr. Wise raised his arms in celebration after breaching the Capitol in a face mask, and he escaped through a window, the complaint added.

Over the past two years, scores of rioters with military experience have been arrested in connection with the Capitol attack. But Mr. Wise is the rare former federal agent to have been charged. The F.B.I. said agents first found Mr. Wise living in New Braunfels, Texas, before he moved to Bend, Ore., in June.

Thomas E. Caldwell, a member of the Oath Keepers who was convicted in November of felony charges stemming from the Jan. 6 riot, had once worked with the F.B.I. And Mark S. Ibrahim, an active-duty agent for the Drug Enforcement Administration, was charged in July 2021 in connection with the riot. His case has not yet gone to trial.

The Justice Department’s investigation of the Capitol attack, already the largest it has ever conducted, has resulted in more than 1,000 arrests, with the possibility of many more to come.

From 2004 to 2017, Mr. Wise worked on counterterrorism matters at the F.B.I. in the New York field office. He was briefly detailed to Libya to help agents investigate the terrorist attack in Benghazi, Libya, in 2012, that killed four Americans. Mr. Wise left the bureau after his supervisors became unhappy with his work, and his career had stalled, a former senior F.B.I. official said.

Mr. Wise later joined the conservative group Project Veritas under the supervision of a former British spy, Richard Seddon, who had been recruited by the security contractor Erik Prince to train operatives to infiltrate trade unions, Democratic congressional campaigns and other targets.

At Project Veritas, according to a former employee with direct knowledge of his employment, Mr. Wise used the code name Bendghazi and trained at the Prince family ranch in Wyoming with other recruits. Mr. Wise took part in an operation against a teachers’ union and apparently left Project Veritas in mid-2018, the former employee said.