On Tuesday, people familiar with the case said that at one point in the summer, after the investigation began pointing to larger potential national security issues, Ms. Kelley tried to get the FBI to drop the matter. The people said she made the request because she was worried about the personal information being provided to investigators.

Ms. Kelley, a 37-year-old volunteer who organized social events for military personnel, developed misgivings after friends in her Tampa social circle urged her to drop the matter, saying the probe would only cause bigger problems, the people familiar with the case said…

Ms. Broadwell, whose extramarital affair with Mr. Petraeus had ended by then, believed that Ms. Kelley may have been a romantic rival, according to this official. Besides the emails sent directly to Ms. Kelley, she also sent a flurry of emails from a pseudonymous account to senior military officials, denigrating Ms. Kelley, the official said.

In the email received by Gen. Allen, Ms. Broadwell—writing under the pseudonym KelleyPatrol—described Ms. Kelley as a “seductress” and warned the general about being entangled in a relationship with her, the official said. A lawyer for Ms. Broadwell didn’t return messages seeking comment Tuesday.