An FBI spokeswoman said the incident was not believed to be linked to terrorism.
The two federal officials said at least one of the people in the car died after the firefight ensued. Both spoke on condition of anonymity because they were not authorised to discuss an ongoing incident on the record.
The NSA is headquartered on the sprawling Army installation near Baltimore.
Thoreson also says FBI agents are doing interviews with witnesses.
Local television showed two damaged vehicles near a gate and emergency workers loading an injured uniformed man into an ambulance.
Aerial news images showed that one of the damaged vehicles was a white SUV marked "NSA Police." Its front end was crumpled, and the hood was up. The other was a dark, unmarked SUV.
The suspect in that case, Hong Young, told police he heard voices directing him to fire on one of the occupied vehicles.
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