Law enforcement officials warned the public Thursday not to "jump to conclusions" in the investigation of a suspect in the murder of 6-year-old JonBenet Ramsey.

District Attorney Mary Lacy, who has led the investigation for Boulder County, Colo., cautioned that there is "much work to be done." Lacy declined at a press conference to disclose details of the case against John Mark Karr, 41, a former second-grade teacher who was arrested Wednesday in Bangkok, Thailand. Karr has not yet been charged in the case.

After his arrest, Karr delivered a stunning public statement in which he admitted his involvement in the murder 10 years ago of the child beauty queen. Karr claimed he drugged and sexually assaulted JonBenet before accidently killing her, Thai investigators said.

JonBenet's body was found beaten and strangled in the basement of her family's Boulder home on Dec. 26, 1996.

Questions began to surface about the details in Karr's statement to investigators, and in an interview with The Associated Press.

Karr's claim that he drugged JonBenet conflicts with an autopsy report filed a day after her body was found, which showed no drugs or alcohol in her system. The report did say she had vaginal abrasions but was inconclusive of whether there was a sexual assault. Cause of death was found to be asphyxia by strangulation.

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Karr also told The Associated Press that he was with JonBenet when she died. However, a California woman who claims to be Karr's ex-wife told San Francisco television station KGO that she was with him in Alabama at the time of the killing. The woman said she does not believe her former husband was involved in JonBenet's murder.

DNA was found beneath JonBenet's fingernails and inside her underwear, but Ramsey family attorney Lin Wood said two years ago that detectives were unable to match it to anyone in an FBI database.

Karr was given a mouth-swab DNA test in Bangkok, according to a law enforcement official who spoke on condition of anonymity. The results of that test were not immediately known. Karr will be given another DNA test when he returns to the United States, the official said.

Lacy, meanwhile, suggested that Karr's arrest may have been forced by other circumstances, including the need for public safety and fear the suspect might flee.

"There are circumstances that exist in any case that mandate an arrest before an investigation is complete," Lacy said. "There is much more work to be done now that the suspect is in custody. Our preference would have been to complete that work out of the public eye. That is obviously not possible this morning."

She refused to say whether authorities were worried Karr was lying about his involvement in the killing. Lacy said Karr has not yet been formally charged, and declined to speculate what charges he might face.

"I'm asking you this morning, let us do our job thoroughly and carefully. The analysis of the evidence in this case continues on a day-by-day, on an hour-by-hour basis as we speak," Lacy said.

More coverage available in FOXNews.com's Crime Center.

Lacy said Colorado investigators were in Thailand, but refused to provide a timeline for Karr's return to the United States.

Karr started work on Tuesday as a second-grade teacher in a Bangkok international school when he was arrested, and had traveled extensively since leaving the U.S. several years ago, Lacy said.

Karr will face charges of first-degree murder, kidnapping and child sexual assault when he is returned to Colorado within the next week, said Ann Hurst of the Department of Homeland Security.

Karr told the AP that he loved JonBenet "very much," and is "very sorry for what happened."

"I am so very sorry for what happened to JonBenet," Karr told The Associated Press in Bangkok. "Her death was an accident."

Asked if he was innocent, Karr said: "No."

He also said that he contacted JonBenet's mother, Patsy, before she died of cancer on June 24 to express his remorse for the killing. Karr said it was his understanding that Patsy Ramsey read letters that he sent to her.

"It's very important for me that everyone knows that I love her very much and that her death was unintentional," said Karr.

Ramsey attorney Wood said Karr had tried to correspond with Patsy Ramsey in the months before her death. Ramsey did not reply, but handed the information over to investigators, helping to link Karr to the case, Wood said.

Patsy Ramsey's family said she knew before she died that authorities were hunting for a potential suspect.

"Patsy was aware that authorities were close to making an arrest in the case and had she lived to see this day, would no doubt have been as pleased as I am," JonBenet's father, said in a statement.

Wood also would not say how the Ramseys knew Karr, although JonBenet was born in Atlanta in 1990, and the Ramseys had lived in the Atlanta suburb of Dunwoody for several years before moving to Colorado in 1991. Karr was a teacher who once lived in Conyers, Ga., another Atlanta suburb, according to Wood.

"John and Patsy lived their lives knowing they were innocent, trying to raise a son despite the furor around them," Wood said. "It's been a very long 10 years, and I'm just sorry Patsy isn't here for me to hug her neck."

Family members have said they believe the Boulder police didn't conduct a thorough enough investigation before they decided JonBenet's parents were somehow to blame.

"I never suspected Patsy or John, they both have very clear consciences and I think we're finding that out now," Patsy Ramsey's sister, Pam Paugh, told FOX News on Thursday.

Paugh said she had never seen Karr before his arrest.

"I've never heard of his name, I've never seen a human being who's looked like him before, I can't recall him from anywhere," she said.

The Denver Post reported that Karr disappeared in 2001 from Petaluma, Calif., where he was living with his wife and three sons, after being released from jail on child pornography charges. His father, Wexford Karr of Atlanta, told the newspaper his son had told him he was behind bars in connection with the Ramsey case.

The Sonoma County, Calif., sheriff's department on Thursday issued a statement saying authorities there began an investigation in April of 2001 into five misdemeanor counts of possession of child pornography. Karr was arrested on April 13, 2001, for these charges and was in court for several months. In December of 2001, a warrant for his arrest was issued for a violation of his supervised release. The Sonoma County Sheriff's Department said it has had no contact with Karr since this warrant was issued.

The Associated Press contributed to this report.