Ingmar Guandique was sentenced to 60 years in prison after being convicted in 2010 of killing and robbing Levy.
Prosecutors in the District of Columbia on Friday dropped their opposition to a new trial.
Guandique's lawyers have appealed the conviction and questioned the credibility of a prosecution witness, Armando Morales, a convicted felon and former gang member. He testified that Guandique confessed to him that he killed Levy.
The U.S. Attorney's Office said the passage of time has made it difficult to elicit accurate testimony in the appeal, so clearing the way for a new trial was done "in the interests of justice."
"We remain firm in our conviction that the jury's verdict was correct and are preparing for a new trial to ensure that Guandique is held accountable," the office said in a statement.
Levy, a 24-year-old California native, was in Washington working as an intern for the Bureau of Prisons when she was last seen on May 1, 2001. Her skull was found over a year later, on May 22, 2002, in Washington's Rock Creek Park.
Levy's disappearance gained national attention after her parents discovered a connection with Gary Condit, who was then a congressman for Levy's California district. Condit was never a suspect in the case, but he was questioned intensively for details about Levy's whereabouts
Police arrested Guandique in February 2009. He was then serving a 10-year sentence for attacking two other women in the park.
Prosecutors asked the judge to order a hearing within two weeks. Evidentiary hearings were held earlier this year in the Guandique case and more are scheduled for May 26, 28 and 29, according to court documents.