The White House cited "grave national security risks and privacy concerns" as the reason for its decision.
Former President Barack Obama voluntarily disclosed more than 6 million records during his presidency.
Critics say the logs allow for monitoring of individuals or groups who may be trying to influence policy.
White House Communications Director Michael Dubke said the administration is following a 2013 federal court ruling that found most of the logs are considered presidential records and are not subject to the Freedom of Information Act (FOIA).