Unconfirmed reports from Peruvian news agencies add that he told them he got enraged when he realized Flores had been looking on his laptop at material about missing Alabama teen Natalee Holloway.
And if that's the case, the developments could leave the door "wide open" to re-opening the investigation into the Holloway disappearance in Aruba five years ago, according to former New York prosecutor Linda Fairstein.
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Holloway was last seen in Aruba with the Dutchman five years ago. He was held and questioned in that case twice, was never charged, and remains the prime suspect.
CBS News Correspondent Elaine Quijano says the confession police say they got as they interrogated him may have been come in a bid for a lighter sentence if he's convicted.
Surveillance video captured van der Sloot, 22, entering his room with Flores, a 21-year-old business student, on Sunday, May 30 - then leaving alone four hours later. Flores' body was found there two days later. Her neck was broken, investigators say.
The Peruvian newspaper la Republica quoted from Van der Sloot's apparent confession: "I did not want to do it. The girl intruded into my private life. She had no right. I went to her and I hit her. She was scared. We argued and she tried to escape. I grabbed her by the neck and hit her."
Police say they plan to take Van der Sloot back to the hotel room in the next few days to re-enact the crime, and he could be charged with murder as early as Tuesday.
Murder convictions in Peru carry a maximum sentence of 35 years in prison.
Although Van der Sloot previously admitted involvement in Holloway's disappearance, that confession came in video captured by a hidden camera by a Dutch TV reporter and was deemed not credible.
This time though, his credibility -- or lack of it -- may not matter. "Whether he confessed, whether that holds up in court, I think this case is really gonna turn on the DNA evidence, the videotape evidence of him going into that hotel room with this young lady, and leaving alone," observes CBS News legal analyst Trent Copeland.
Fairstein, who headed the sex crimes unit of the Manhattan District Attorney's office for more than 25 years, agrees.
She says if Van der Sloot indeed revealed he killed Flores because she'd seen info about Holloway on his laptop, "I think these are wide open doors (to restarting the Holloway probe). And in so many ways, whatever information they originally had about that case that caused them to arrest him, let him go, re-arrest him, you have other things.
"There were young men originally picked up who had perhaps been accomplices in disposing of the body. He was a threat to them at that time. He was more powerful, he was richer, he was from a more established family. So, one would hope, as a prosecutor, you would go after now these guys. He's behind bars. Maybe they're gonna come back with a story now and cooperate. So many things can change and perhaps improve the dynamic of the cold case."
As for the confession police say they got, "I think the confession is important. It's helpful in any case, but so unlike the Holloway case, there's so much direct physical evidence in this case. It happened in his room, as opposed to a case where a body was never found and was outside. He's seen going into the room with Flores. He comes out alone. So, for a prosecutor, for a police investigator, a lot of good physical evidence. A confession, if true, is icing on the cake."