Mr. Rothstein said that investigators had searched five apartments and several cars that Mr. Taherzadeh and Mr. Ali had used. He said they found equipment and paraphernalia usually associated with law enforcement, including body armor, gas masks, zip ties, hand-held radios, a drone like the ones used by S.W.A.T. teams, Homeland Security patches, 40 to 50 rounds of ammunition, weapon stocks and documents that were stamped “law enforcement sensitive.”

Mr. Taherzadeh told Magistrate Judge G. Michael Harvey in court on Thursday that he had completed “some college” at Georgetown University. Michelle Peterson, a federal public defender who represented both men, said they planned to ask to be released at the hearing on Friday.

If convicted on the impersonation charge, they face up to three years in prison and a $250,000 fine.

According to the affidavit, Mr. Taherzadeh provided members of the Secret Service and a Homeland Security employee rent-free apartments, iPhones, surveillance systems, a drone, a flat-screen television, a generator and case to store an assault rifle.

Mr. Taherzadeh also offered them what he described as “official government vehicles.”

The White House did not immediately respond to a request for comment on Thursday. Michael LaRosa, a spokesman for Dr. Biden, and the Homeland Security Department referred questions to the Secret Service.

In a statement, a spokesman for the Secret Service said that the agency was working with investigators and that the employees involved in the case had been restricted “from accessing Secret Service facilities, equipment, and systems.”

“The Secret Service adheres to the highest levels of professional standards and conduct and will remain in active coordination with the Departments of Justice and Homeland Security,” the spokesman, Kang Lee, said.