Mr. Garland provided no details. But the person briefed on the matter said investigators had been concerned about material from what the government calls “special access programs,” a designation even more classified than “top secret” that is typically reserved for extremely sensitive operations carried out by the United States abroad or for closely held technologies and capabilities.

Government officials have expressed concern that allowing highly classified materials to remain at Mr. Trump’s home could leave them vulnerable to efforts by foreign adversaries to acquire them, according to another person familiar with the Justice Department’s thinking.