WASHINGTON — The email described a deteriorating situation in Libya, with snipers shooting people in the streets as rebels tried to unseat President Muammar el-Qaddafi and worried American diplomats in the midst of a “phased checkout” from Benghazi. It arrived in the private email account of Secretary of State Hillary Rodham Clinton, one Sunday morning in April 2011, with unforeseen consequences.

That email, which included an update from the Africa Command of the Department of Defense detailing Libyan military movements, is part of the evidence that law enforcement officials say the F.B.I. is now examining as it tries to determine whether aides to Mrs. Clinton mishandled delicate national security information when they communicated with their boss.

The Libyan dispatch, written by an aide to Mrs. Clinton and then forwarded to her by Huma Abedin, one of her top advisers, should have been considered classified, according to intelligence officials. And, they say, other emails to Mrs. Clinton they have found, including one addressing North Korea’s nuclear weapons system and a third discussing United States drone strikes in Pakistan, should have been marked “Top Secret.”

There is no evidence that any of the emails — a small portion of some 60,000 that Mrs. Clinton sent or received as secretary of state — were hacked or caused any harm to American interests, and law enforcement officials have said she is not a target of their investigation. But one of the questions they are seeking to answer is whether her aides or other State Department officials broke federal rules or laws when they sent her information. And arriving at an answer will not be simple, given the complex and often conflicting views of just how diplomatically fragile the information conveyed in the emails actually was.