WASHINGTON—The National Security Agency, responding to a Freedom of Information Act lawsuit, has released heavily redacted reports detailing its employees’ violations of individual Americans’ privacy in the broad surveillance net cast after the Sept. 11, 2001, terror attacks.

The agency was required by executive order to file the reports with the President’s Intelligence Oversight Board. But the quarterly and annual reports covering NSA activities from 2001 to 2013 were publicly released Wednesday only after the American Civil...