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BOULDER, Colorado (CNN) -- John Mark Karr told the world he killed JonBenet Ramsey almost 10 years ago in her Boulder home, but DNA evidence points to an unidentified killer.
Karr, the 41-year-old teacher, was hunted down halfway around the world and brought back to Colorado last week.
After his arrest in Bangkok, Thailand, on August 16, he freely -- and repeatedly -- said he was with JonBenet when she died in December 1996, although he insisted that her death was an accident and that he "loved" her.
Karr, who had a longtime fascination with the Ramsey case, also gave investigators graphic details about the condition of the 6-year-old's body that were not publicly known, a U.S. law enforcement official said. (Watch how evidence belied Karr's story -- 1:17)
But the case against Karr started to crumble Saturday, when a forensic expert determined that DNA mixed in with a spot of JonBenet's blood found on her underwear did not belong to Karr.
Prosecutors said that finding contradicted Karr's statements about what he did to the girl.
"If Mr. Karr's account of his sexual involvement with the victim were accurate, it would have been highly likely that his saliva would have been mixed with the blood in the underwear," Boulder County prosecutors said in a motion they filed Monday to dismiss Karr's arrest warrant.
"No evidence has developed, other than his own repeated admissions, to place Mr. Karr at the scene of the crime," the motion said.
Prosecutors also were swayed by what they described as "strong circumstantial" evidence provided by Karr's family that he was with them in Georgia during Christmas 1996, when JonBenet was struck in the head and strangled with a garrote in her family's Boulder home.
"That's what we've been saying all along," said Larry Garrison, a spokesman for Karr's family.
Though cleared in the Ramsey case, he remained in the Boulder County Jail on Monday night after California authorities sought his extradition to face five misdemeanor counts of possessing child pornography. Karr skipped bail on those charges in 2001.
Colorado District Court Judge Roxanne Bailin set Karr's extradition hearing for 4 p.m. (6 p.m. ET) Tuesday.
Karr's arrest in Thailand came five days after law enforcement officials were able to trace his location and identity, using e-mail correspondence and phone calls between him and Michael Tracey, a University of Colorado journalism professor who had been communicating with Karr since 2002.
Starting in April, Karr, who used the pseudonym "Daxis," began "to claim more personal knowledge" about JonBenet's killing, including admitting "personal responsibility" for her death, prosecutors said. He also sent portions of a manuscript to Tracey in which Karr claimed to have accidentally asphyxiated the girl after losing track of time during "sexual activities."
At one point, in an effort to locate Karr, investigators got Tracey to convince him to call JonBenet's parents, John and Patsy Ramsey.
"Law enforcement agencies cooperated in an unsuccessful effort to trace that call," prosecutors said Monday in their motion.
The date of the call was not disclosed. Patsy Ramsey died June 24 from ovarian cancer.
Despite the lack of solid evidence, authorities said arresting Karr was the only way to find out if he was telling the truth and to keep him from going into hiding.
Prosecutors said they also feared Karr could be a danger because he had expressed "sexual interest in specific young girls" at a Thai school where he had taken a job as a teacher.
Authorities were able to confirm that Karr "was having personal involvement with at least one of the girls he had previously identified as the target of his personal and sexual interest," according to the prosecution motion.
Karr's public defender in Boulder, Seth Temin, questioned the prosecution's actions.
"We're deeply distressed by the fact they took this man, dragged him back here from Bangkok, Thailand, with no forensic evidence confirming the allegations against him and no independent factors leading to a presumption that he did anything wrong," Temin said.
Colorado Gov. Bill Owens railed against Boulder County District Attorney Mary Lacy, accusing her of wasting thousands of taxpayer dollars in the Karr case.
"Unfortunately, the hysterics surrounding John Mark Karr served only to distract Boulder officials from doing their job, which should be solving the murder of JonBenet Ramsey," Owens said in a statement. "Mary Lacy should be held accountable for the most extravagant and expensive DNA test in Colorado history."
For the Ramsey family, hope of closure in the case was dashed.
"It's another bump in the road for us emotionally, but I think we saw Lady Justice put her gavel down today," said Pam Paugh, Patsy Ramsey's sister. "I don't think that this story is over yet, and I think, again, patience is the prudent thing to desire at this point."
In a statement Monday, Lacy said that "our role in the investigation of JonBenet Ramsey's murder has been to follow up on all legitimate leads that we have received from law enforcement and concerned citizens."
"The case is not closed, and we will continue to investigate leads and pursue justice," she said.
CNN's Susan Candiotti and Tracy Sabo contributed to this report.