Embattled Rep. Gary Condit, D-Calif., called missing intern Chandra Levy's parents Saturday night, but they deferred him to their new, high-profile Washington lawyer, sources close to Levy told Fox News.

Condit, 53, made the phone call amidst a sea of new allegations, including that in the months prior to her disappearance April 30, a smitten Levy saw her married hometown congressman more than once a week and called him on a private number that would automatically page him.

Friends of the congressman are now saying the 24-year-old intern was infatuated with her representative. They insist, however, that whatever relationship existed between the two had nothing to do with her disappearance.

Sources close to Condit said the congressman's supporters and advisers have been pushing him to hold a press conference as early as this week to discuss the nature of his relationship with Levy, with whom he has denied having had an affair. Condit may do so, although he fears fanning the flames of this tabloid-friendly story, the sources said.

Condit is also talking with TV networks about doing an interview to discuss the disappearance, the New York Post reported Sunday. The newspaper stated that he would prefer to appear on a news magazine like CBS' 60 Minutes or ABC's 20/20 and have a one-on-one interview — a setting similar to the one former President Bill Clinton used to discuss his affair with Gennifer Flowers.

The spotlight has shone more harshly on Condit since Thursday, when The Washington Post reported that a close relative of the Levys told Chandra's mother in April that Chandra said she was having a romantic relationship with the congressman.

Condit has since hired his own high-powered lawyer, Joseph Cotchett. Cotchett is seeking retractions from several media outlets — including The Washington Post — for a story quoting police as saying Chandra spent the night at Condit's Washington apartment.

Condit, through a written statement and through his lawyer, has said that he and the intern were nothing more than good friends.

Levy, a graduate student at UCLA, was finishing up an internship at the Bureau of Prisons in Washington when she vanished. Her parents said she was on her way back to their Modesto, Calif., home to attend graduation ceremonies. Police found her bags packed and ready to go in her Washington apartment.

Levy met Condit last October, when she went to his office to visit a friend who was working there as an intern. The handsome politician is nicknamed "Mr. Blow Dry" in Congress for his well-coiffed hairdo, and is known for his youthful behavior, including a penchant for rock concerts and an apartment in a hip, bohemian neighborhood.

Condit is the father of two grown children. His wife, who has been reported to have health problems, lives in California.

Levy was last heard from May 1, when she e-mailed her parents.

In interviews, Levy's parents have indicated that they believe people who have information about the disappearance are under pressure not to step forward.

The couple plans to fly to Washington this week to meet with their new attorney, who will help guide them on what they should or shouldn't say as police continue their investigation. The Levys also plan to meet with D.C. police and the FBI, and they're considering holding a press conference.

Fox News' Collins Spencer and the New York Post contributed to this report