Rep. Gary Condit is ready to talk to the FBI, sources close to the bureau said Tuesday.

The California Democrat agreed to help the FBI create a psychological profile of missing federal intern Chandra Levy when an agent new to the case offered to conduct the interview without Washington, D.C., police present.

Washington police have been trying to arrange a fourth interview with the married 53-year-old congressman, who admitted in his third interview, after two months of denials, that he indeed had had an affair with the 24-year-old Levy.

The sources, speaking on condition of anonymity, said the FBI profiling session could happen as early as this week, Condit's schedule permitting.

Levy disappeared May 1 from her Washington apartment, soon after her internship with the Bureau of Prisons abruptly ended when she revealed her graduate studies at the University of Southern California had technically finished. The police are treating her disappearance as a missing-persons case and have insisted that Condit is not a suspect and that he is under no obligation to talk to them.

Condit has denied any role in Levy's disappearance. His lawyers have said he passed a self-arranged lie-detector test administered by a former FBI expert, a test the D.C. police have dismissed as meaningless.

Agent Bradley Garrett, who specializes in drawn-out cases for the FBI's Washington field office, arranged the profile session Tuesday in discussions with Condit's lawyers, the sources said.

Garrett indicated to Condit's legal team that the FBI was taking a fresh look at Levy's disappearance, the sources said. They said the profilers would seek information from Condit and others on where Levy might have gone, whom she might have seen or any reason she might have been vulnerable when she disappeared.

Meanwhile, Condit earned some bitter words from a fellow "Blue Dog" Democrat and friend.

"I will say that through his actions and behaviors," Rep. Charles Stenholm, D-Texas, said in a prepared statement, "Congressman Condit has brought controversy and discredit to his family, his district and the Congress."

Stenholm stopped short of calling for Condit to resign, saying "ultimately it remains the prerogative of each congressional district to elect who they wish." Stenholm added that he is reserving judgment in case the House conducts an ethics investigation into Condit's behavior.

Stenholm and Condit have been longtime leaders of the "Blue Dog" conservative Democrats in Congress, who sometimes vote with the GOP on social and fiscal issues.

Levy's parents this week released new photos and video footage of their daughter, seeking to keep attention focused on her disappearance. Police searched various D.C. parks Tuesday without success.

D.C. police spokesman Sgt. Joe Gentile said search teams will resume work Wednesday, once again combing through Rock Creek Park near Levy's apartment, as well an area behind a golf course in another part of the city.

The police would specifically like to talk to Condit about an empty watch box he reportedly threw out in a suburban park the morning before his apartment was searched by investigators looking for clues to Levy's whereabouts.

Sources have told Fox News one of Condit's senior aides drove the congressman to the Alexandria, Va., park where he discarded the box. Fox News has learned the box had contained a Tag Heuer watch given to Condit by a 29-year-old California woman who worked for him in an administrative position in 1994.

Police do not believe the watch box has any relation to Levy's disappearance, officials said.

Investigators have also become frustrated with the silence of some of Levy's neighbors, who still have not responded to appeals for help in finding the missing woman.

Executive Assistant Police Chief Terrance Gainer said there are still "far too many people, more than a handful," in Levy's apartment building who have yet to be interviewed about the 24-year-old graduate student's disappearance.

"But this is America" Gainer added, "and absent acting like jack-booted thugs, we can't force them to talk to us."

The reward for information leading to Levy's whereabouts has reached $200,000, with part of that sum donated by Condit himself, a representative for the Carole Sund Foundation told ABC's Good Morning America Tuesday morning.

Fox News' Rita Cosby and the Associated Press contributed to this report