Court records show the hearings have taken place behind closed doors but neither prosecutors nor defense lawyers have revealed the purpose of the sessions.
A spokesman for the U.S. Attorney's office, which is handling the case, didn't immediately return a call seeking comment Friday.
Several media organizations, including The Associated Press, are petitioning to open the proceedings. The next hearing takes place on February 7.
Ingmar Guandique was convicted in 2010 of killing Levy, whose remains were found in Washington's Rock Creek Park. The case relied largely on testimony from an inmate who served time in prison with Guandique.
Guandique was sentenced to 60 years in prison.
The case captured the nation's attention because of Levy's relationship with California congressman Gary Condit. Though Condit, who is no longer in Congress, was interviewed by investigators, authorities eventually ruled him out as a suspect and no longer believe he had anything to do with her death.
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Levy's father, Robert Levy, told KGO-TV in San Francisco that he has not been told what's going on. He said Guandique was a "convicted rapist and an illegal alien."
But, he added, "if he's innocent of murder, he shouldn't be in jail for it."
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