While he did not identify any, he was evidently referring to two emails that one of Mrs. Clinton’s close aides, Monica R. Hanley, sent to prepare her for telephone calls with foreign leaders, according to a State Department official familiar with the matter, who spoke on condition of anonymity to discuss classified information.

One email, dated Aug. 2, 2012, noted that Kofi Annan, the former secretary general of the United Nations, was stepping down as special envoy trying to mediate the war in Syria. A second one, sent in April 2012, discussed Mrs. Clinton’s call to the newly inaugurated president of Malawi.

Each was marked with a small notation, “(C),” indicating it contained information classified as “confidential.”

Other paragraphs in the note about Mr. Annan’s resignation were marked “(SBU),” for “sensitive but unclassified.” That designation appears in more than 1,000 of the 30,000 work-related emails that Mrs. Clinton turned over to the State Department, including some later “upgraded” to higher levels of classification. The official said that the notations were part of “a standard process” when preparing a phone call, which would be “confidential” until it occurred and then considered unclassified.

Far more serious were those that were unmarked, according to Mr. Comey. He referred at one point to eight chains that were classified as “top secret,” and at another point to seven with the additional designation as “special access programs.” Only a small number of officials are allowed access to those programs, which are the nation’s most sensitive intelligence operations.

“Those chains involved Secretary Clinton both sending and receiving emails about those same matters,” he said.

Mr. Comey did not detail any of the information contained in the emails, but the State Department announced in January that it would not release to the public 22 emails contained in seven chains of emails and replies, even in a redacted form, as thousands of others have been over the last year. Those emails have been widely reported to include information about the Central Intelligence Agency’s program to use drones to track and kill terrorism suspects.