Instead, reports CBS News Correspondent Jeff Glor, the 22-year-old Dutchman refused to discuss the case and recanted his original confession.
Van der Sloot is also the chief suspect in the 2005 disappearance in Aruba of Alabama teen Natalee Holloway.
The Peruvian judge went to the infamous Miguel Castro Castro Prison to interrogate van der Sloot about the death of Flores, a 21-year-old business student, in his Lima hotel room May 30.
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But according to court documents, van der Sloot not only refused to discuss his case, he repeated his claim that his original confession was coerced, and formally requested it be declared invalid.
"He is certainly delaying the process," says former prosecutor Beth Karas. "He's going to fight every battle that he can under Peruvian law."
Graphic crime scene photos obtained exclusively by CBS News show a severely beaten Flores, her body badly bruised, her clothes stained with blood.
Investigators claim surveillance video from the day of the murder shows van der Sloot . He's seen leaving the hotel room, returning minutes later, coffee cups in hand, and asking a porter to open the door for him. Peruvian police allege he was hoping the porter would discover Flores' body, enabling van der Sloot to claim she was murdered while he was out getting the coffee.
Of his confession, van der Sloot contended to a Dutch newspaper, "In my blind panic, I signed everything, but didn't even know what it said."
Still, legal experts say the case against van der Sloot is strong, even without the confession. "There's a lot of evidence," says Karas, "tying him to the room, which was in his name, to the woman he's seen on video with, to the actual scene -- so, it looks like there can be a case proven even without a statement."
In addition, a Dutch newspaper says van der Sloot is bragging in prison about all the marriage proposals he's been getting.
International Criminal Defense Attorney Dan Conaway explained on "The Early Show" Tuesday that van der Sloot refusing to talk to the judge isn't actually as bad as it sounds: Peru has an inquisitorial justice system, which means the judge acts in much the same capacity as the prosecutor, asking questions, investigating, etc. So van der Sloot keeping tight-lipped is really just his lawyers correctly telling him to keep quiet during the investigation.
Conaway says he doesn't understand why his lawyers are fighting to get his confession thrown out. Considering all the circumstantial evidence, Conaway points out, it seems like this is pretty much a done deal, and at least the confession shows that van der Sloot is co-operating with authorities. And that would help him if this comes to a deal -- it would help with his sentence.
Ultimately, though, Conaway says he doesn't think the confession will be thrown out, because van der Sloot did have counsel present when he made it, though the counsel was court-appointed and not his own.
But, Conaway adds, his lawyers are being wise in having him stop talking in general, as evidenced by him not answering the judge's questions Monday. There are so many rumors and stories circulating, some of which have apparently come from van der Sloot himself (regarding both Holloway and Flores), so it's important that his lawyers put a cap on that.
Conaway also points out the process isn't going to be short -- in Peru, things move very slowly. He says he doesn't expect the next step, whether it's a plea deal or a trial date being set, to happen for at least another six months. And if it goes to trial, that probably wouldn't get started for roughly a year-and-a-half.
It's also important to remember, Conaway notes, that in the Peruvian system, the standard for guilt is different - there's a lower threshold there for proving guilt than in the United States.