A previously confidential directive by Biden administration lawyers lays out how military and spy agencies must handle personal information about Americans when using artificial intelligence, showing how the officials grappled with trade-offs between civil liberties and national security.

The results of that internal debate also underscore the constraints and challenges the government faces in issuing rules that keep pace with rapid advances in technology, particularly in electronic surveillance and related areas of computer-assisted intelligence gathering and analysis.

The administration had to navigate two competing goals, according to a senior administration official, Joshua Geltzer, the top legal adviser to the National Security Council: “harnessing emerging technology to protect Americans, and establishing guardrails for safeguarding Americans’ privacy and other considerations.”

The White House last month held back the four-page, unclassified directive when President Biden signed a major national security memo that pushes military and intelligence agencies to make greater use of A.I. within certain guardrails.

After inquiries from The New York Times, the White House has made the guidance public. A close read and an interview with Mr. Geltzer, who oversaw the deliberations by lawyers from across the executive branch, offers greater clarity on the current rules that national security agencies must follow when experimenting with using A.I.