Broadwell, a former Harvard University researcher who focused her dissertation on Petraeus's military career, hired longtime Washington criminal defense attorney Robert Muse, the lawyer said Monday.
Attempts to reach Broadwell since Petraeus resigned Friday have been unsuccessful.
Federal investigators have said Broadwell sent a series of e-mails to Kelley from an anonymous account telling her to stop behavior she saw as overly friendly toward Petraeus, or she would be exposed. The law enforcement officials, who spoke on condition of anonymity, said the e-mails indicate Broadwell felt jealous of the other woman.
The e-mails did not specifically cite Kelley's friendship with Petraeus, according to a person close to Kelley, who also spoke on condition of anonymity. She did not know who was sending them and why.
Kelley contacted her friend in the FBI, who took her concerns to the bureau. Investigators were later able to trace the emails to Broadwell.
In Broadwell's account, investigators found emails from Petraeus, and given the personal nature of some of them, believed at first that they were being sent by someone who had hacked into the CIA director's account.
Kelley was informed that Broadwell was the sender, although she told investigators that she did not know the woman, according to the person close to Kelley.
At some point, Kelley told Petraeus about the emails and named Broadwell as the person who had sent them. That may have prompted the CIA director to send his own emails to Broadwell, telling her to stop the harassment, the law enforcement officials said.
People close to Petraeus say his affair with Broadwell ended four months ago, around the time he emailed her about the harassment.
When confronted by FBI agents about the emails, Broadwell acknowledged the affair with Petraeus and turned over her computer to investigators. Petraeus, who has been married to Holly Petraeus for 38 years, also acknowledged the extramarital relationship in his interview with the FBI.
By late summer, the FBI informed the Justice Department about the case. Federal prosecutors decided there was not enough evidence to file charges against Petraeus, who was interviewed by investigators during the week of Oct. 21. Broadwell was interviewed by agents for the last time the week before.
The FBI agent in Tampa had been taken off the investigation by that time. He was frustrated by the investigation's apparent lack of progress, according to the person close to Kelley.
But the agent recently got in touch with the Washington office of Rep. Dave Reichert, R-Wash., to express concern. Reichert then contacted Rep. Eric Cantor, R- Va., the House Republican leader.
"I was contacted by an F.B.I. employee concerned that sensitive, classified information may have been compromised and made certain Director Mueller was aware of these serious allegations and the potential risk to our national security," Cantor said in a statement issued Saturday. He referred to FBI Director Robert Mueller.