Secret Service investigators were trying to verify the employee’s account on Tuesday as they interviewed people he said he had contacted in the hours before the episode. They were also examining his text messages and phone records as well as analyzing video footage from cameras around the apartment where the man said he had operated the drone.

Although planes are restricted from entering the airspace around the White House and it is illegal to operate a drone in Washington, it is unclear whether the man will be charged with a crime. Some Secret Service officials believe he should be prosecuted in an effort to deter others.

Officials at the geospatial-intelligence agency — which is based near Springfield, Va., as part of the Defense Department — prefer to stay out of the headlines. The agency uses satellites to gather data for the military and other law enforcement and intelligence agencies. According to its website, the agency played a role in helping locate the compound in Pakistan where Osama bin Laden was hiding. Using high-resolution photographs of the compound taken by satellite, the agency then helped create a replica of the compound so that a team of Navy SEALs could rehearse the raid in which bin Laden was ultimately killed in 2011.

The website says the agency also helped discover atrocities in Kosovo, provided support for intelligence operations during the Olympics and assisted in the response to Hurricane Katrina.

James R. Clapper Jr., the current director of national intelligence, became the head of the agency, then called the National Imagery and Mapping Agency, just days after the Sept. 11, 2001, attacks.

The episode could prove embarrassing to the head of the geospatial agency, Robert Cardillo. Until he took over the agency last October, Mr. Cardillo was the deputy director of national intelligence, who frequently provided Mr. Obama with his daily intelligence briefing.

The drone incident is the latest to raise questions about the security of the White House. It occurred four months after a man with a knife climbed over the White House fence and made it deep inside the building before officers tackled him. In 2011, a gunman three-quarters of a mile away from the White House fired shots that hit the building while one of the Obama daughters was home.