While the new letter was clear as it related to Mrs. Clinton, Mr. Comey’s message was otherwise vague. He did not say that agents had completed their review of the emails, or that they were abandoning the matter in regard to her aides. But federal law enforcement officials said that they considered the review of emails related to Mrs. Clinton’s server complete, and that Mr. Comey’s letter was intended to convey that.

One senior law enforcement official said that as recently as Friday, it was not clear whether the review would be completed by Election Day. But after days of working in shifts around the clock, teams of counterintelligence agents and technology specialists at the bureau’s headquarters in Washington finished their examination of the thousands of emails. Officials had decided to make their decision public as soon as they had reached it, to avoid any suggestion that they were suppressing information.

According to the law enforcement official, many of the emails were personal messages or duplicates of ones that the bureau had previously examined during the original inquiry.

Brian Fallon, a spokesman for Mrs. Clinton, said in a post on Twitter that the campaign had always believed she would be cleared of any wrongdoing.