Specifically, the inspector general told members of Congress that two emails should have been classified as top secret, with one of them designated “TOP SECRET//SI//TK/NOFORN.” Officials familiar with the nomenclature said that “SI” stood for “special intelligence,” usually indicating an intercepted communication, and that “TK” was routinely used as an abbreviation for Talent Keyhole, showing that the communication or an image was obtained from a satellite.

Attached to the memo — which was publicly released by Senator Charles E. Grassley, the Iowa Republican who is chairman of the Senate Judiciary Committee — were copies of two of Mrs. Clinton’s emails that Mr. McCullough said contained classified information. Those emails were not released publicly.

The State Department has questioned whether the determination by Mr. McCullough is correct. Nevertheless, the findings are consistent with the view of some federal officials that the State Department is not rigorous enough in handling classified national security information.

In an unusual move, the F.B.I.’s inquiry is being led out of its headquarters in Washington, blocks from the White House. Nearly all investigations are assigned to one of the bureau’s 56 field offices. But given this inquiry’s importance, senior F.B.I. officials have opted to keep it closely held in Washington in the agency’s counterintelligence section, which investigates how national security secrets are handled.

The investigation into Mrs. Clinton’s emails has its roots in her decision to use only a private email account for her official business when she was secretary of state, an unorthodox decision that gave her some control over what was made public. She faced criticism when her use of the account became known this year, and after deleting what she said were more than 31,000 personal emails, she turned over more than 30,000 work-related emails for the State Department to make public.

Mrs. Clinton has said that her emails contained no classified information — having classified information outside a secure government account is illegal — and that she is fully cooperating with the investigation. But in reviewing a sampling of the emails for potential security breaches, Mr. McCullough said he found four out of 40 that contained classified information, though perhaps stripped of any indication that it was of classified origin.

According to current and former State Department officials who worked with Mrs. Clinton, most classified information was routed to classified government servers in her office, where it was printed out for her review. Her predecessor, Condoleezza Rice, often operated the same way.