WASHINGTON—The government said Monday it had cracked a terrorist’s iPhone without Apple Inc.’s help and is seeking to drop its legal case to force the tech giant to unlock the device.

The move was announced in court papers filed Monday in a dispute over a phone seized in the investigation of a Dec. 2 terror attack in San Bernardino, Calif. The filing signals a temporary reprieve from a high-stakes fight between Washington and Silicon Valley over privacy and security in the digital age. For now, the Federal Bureau of Investigation...