It was unclear what the new information is, and prosecutors said it should be sealed because of safety concerns for the witness.
At the request of the prosecution, hearings will be closed and the attorneys in the case are under a gag order, the Post reported.
Guandique's hearing Thursday was his first since being sentenced to 60 years in prison, the report said.
Guandique, 30, was escorted into the courtroom in shackles and appeared thinner than he did at his eight-week 2010 trial, the Post said.
The Salvadoran was convicted of first-degree murder.
Levy's remains were found in Washington's Rock Creek Park in 2002, the year after the Federal Bureau of Prisons intern disappeared.