John Mark Karr, the suspect picked up in Thailand who has confessed to killing JonBenet Ramsey, will be back in the United States by late Sunday night, FOX News has confirmed.

Karr will fly out of Bangkok on a Thai Airways flight 794 scheduled to leave Sunday evening, bound for Los Angeles.

When back on American soil, Karr will stay in Los Angeles for one to two days while his paper work is process so he can be extradited to Boulder, Colo., to face charges of murder, kidnapping and sexual assault of a child.

"The tickets for John Mark Karr's departure are ready," Thailand's immigration police chief, Lt. Gen. Suwat Tumrongsiskul, told reporters. "He is leaving for the United States on Sunday evening." Suwat did not say the number of U.S. officials who would accompany him.

U.S. Homeland Security official to Thailand Ann Hurst, along with another unnamed U.S. official, arrived Saturday at the jail where Karr is being held in Bangkok.

After meeting with Karr, Hurst told FOX News in an exclusive interview that he is "a very complex person" and displayed "a myriad of emotions" in their interview.

"He showed a bit of surprise at first but then when we read that we had a warrant for his arrest for the murder of JonBenet Ramsey, he seemed surprised, but not too shocked," Hurst said.

Karr, 41, remained under detention in Bangkok on Saturday, three days after his stunning claim that he was with the 6-year-old beauty pageant princess when she died in her family's home.

Karr's arrest came with the help of Operation Predator, an arm of the U.S. Immigration and Customs Enforcement that targets child predators who may be outside of the United States. The agency contacted the Royal Thai police with only the alias with which Karr e-mailed a Colorado professor.

Within a week, officials were monitoring Karr in his rented apartment, and a week after that, Karr was brought into custody on a visa violation.

FOXNews.com's photo essay on John Mark Karr

After his arrest, he told reporters he was alone with JonBenet when she died in the basement of her home on Dec. 26, 1996, but that her death was an accident.

"I am so very sorry for what happened to JonBenet," Karr told The Associated Press on Thursday. "It's very important for me that everyone knows that I love her very much, that her death was unintentional, that it was an accident."

U.S. officials, the only ones to have actually interrogated Karr, have been silent about what he told them, citing his right to privacy and legal procedures.

Meanwhile, slices of Karr's globe-trotting life as a teacher began to emerge as he remained detained in an immigration jail in Thailand's capital.

An administrator at an elite Bangkok school described Karr as articulate and polite, but too strict, and said he was fired after two weeks on the job.

"John Karr came to us with a good resume and with credentials, but then we allowed him a trial (period) with students, we found he was too strict," said Banchong Chompowong, an administrator at Bangkok Christian College's elementary school.

Experts said the questions surrounding Karr's story put more pressure on corroborating evidence such as DNA.

Timeline: The JonBenet Ramsey Murder Investigation

"They either have a miss or a match on the DNA," former Denver prosecutor Craig Silverman said. "If it's a miss, the prosecution has serious problems. If it's a match, then it's game, set and match for this case. Couple the DNA with the kooky confession and it's enough for most people to convict."

"The bottom line is that they now have a confession and until and unless they can corroborate that confession with either physical evidence or strong circumstantial evidence, that's all they have," said Scott Robinson, a Denver attorney who has followed the case from the beginning.

"I am so very sorry for what happened to JonBenet," Karr told The Associated Press on Thursday as police brought him through his guesthouse to collect belongings following his arrest. "It's very important for me that everyone knows that I love her very much, that her death was unintentional, that it was an accident."

Suwat, the Thai police general, said a Thai officer asked Karr why he had sex with a 6-year-old girl.

"He said that at the time it was just a blur. He said they were lovers," Suwat told The Associated Press.

Suwat said Karr, whom he described as "quiet and kind of strange," now wanted to go back to the United States to fight the case.

He said U.S. authorities were preparing documents and plane tickets for the return journey. The departure could take place at any time, he said.

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

The divorced father of three children, once detained on charges of possessing child pornography, apparently traveled the world searching for teaching jobs. Suwat said the suspect had visited several Asian countries in recent years, but provided no details.

In Taiwan, the National Police Administration said Friday that Karr entered the country in August 2005 and left two months later. The NPA didn't know whether Karr taught during his stay and had no indication he engaged in any criminal behavior.

Karr was arrested a day after he began teaching second grade in Bangkok, District Attorney Mary Lacy told reporters in the Colorado.

In June, he taught first graders at Bangkok Christian College, Thailand's oldest private school, established by American Presbyterian missionaries in 1852. The school caters to about 5,500 male students in 12 grades and is regarded as one of Bangkok's top private schools.

"He was qualified to be a teacher. He had a diploma and has experience in teaching in Bangkok for some time," said Banchong, assistant director of the school's English immersion program.

He was very presentable, Banchong said. But he was dismissed after two weeks when parents complained that he was too strict with their children, he said.

Banchong said that Karr also had taught at St. Joseph's Convent, another prestigious elementary and secondary Thai school. But officials there refused to talk to reporters.

Karr will be taken within the week to Colorado, where he will face charges of first-degree murder, kidnapping and child sexual assault, U.S. officials in Bangkok have said.

Denver attorney Larry Pozner, past president of the National Association of Criminal Defense Lawyers, said there were "serious questions" about the case.

"I hope we have found the murderer of JonBenet, but I have not heard the evidence that compels that conclusion," he said.

FOX NEW's William LaJeunesse and the Associated Press contributed to this report.

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