The Trump administration scrambled to minimize fallout on Thursday after exposing personal information, including Social Security numbers, of hundreds of congressional staff members, intelligence researchers and even an ambassador when releasing files pertaining to the death of President John F. Kennedy.

The exposure of personal details, as well as long-guarded secrets about Cold War spycraft, came as a result of the National Archives uploading 64,000 pages of documents related — some very tangentially — to Kennedy’s 1963 assassination.

White House officials acknowledged on Thursday that it was only after the papers were made public that they began combing through them for exposed details.

On Wednesday, the White House ordered that the pages be combed for exposed Social Security numbers, and officials directed the Social Security Administration to issue new numbers to the affected people, according to a senior administration official, in an extraordinary response to mitigate the potential harm of the disclosures. They will also be offered free credit monitoring.

Normally, personal information like names, Social Security numbers and home addresses are scrubbed from declassified files.

William A. Harnage, a former government contractor, learned from a reporter that the administration had released his personal information in a file from 1977. “I consider it almost criminal,” said Mr. Harnage, 71.

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