The U.S. Department of State recommends you first report a lost or stolen passport to the local police in the area in which the loss or theft occurred. Then immediately contact the nearest U.S. Embassy or Consulate from this list. In order to protect yourself from identity fraud it is important to report a lost or stolen passport immediately. Start the replacement passport process as soon as possible. (Also see, How do I get an emergency replacement passport if I am traveling?) If you find it after reporting it lost or stolen, it is invalid once reported as missing and can no longer be used for travel.
For more information, visit the US embassy website