Thailand hopes to deport a suspect in the JonBenet Ramsey murder to the US as early as this weekend, officials say.
John Mark Karr says he was with JonBenet when she died
John Mark Karr, 41, says he was with the child beauty queen when she died, but insists her death was an accident.
The six-year-old was beaten and strangled in her Colorado home 10 years ago.
The US district attorney investigating the case has warned against speculation about the possible guilt of Mr Karr.
"John Mark Karr is presumed innocent," Mary Lacy said, adding that the public must not "jump to conclusions".
Officials at one school in Thailand have said Mr Karr was asked to leave after a two-week trial because his discipline methods were too tough.
"John Karr came to us with a good resume and with credentials, but then we allowed him a trial with students - we found he was too strict," said an official at the Bangkok Christian College.
Just before his arrest, Mr Karr had started work in another Bangkok international school.
Thai authorities have called for tougher background checks for employees at international schools, the AFP news agency reported on Friday.
Reviews of qualifications and stricter enforcement of visa regulations were among the tougher screening measures that would be introduced, said Jakrapob Penkair, deputy secretary to the prime minister.
"Currently most of the teachers in international schools are illegally working on tourist visas," he said.
"So to prevent such incidents in the future, we must take pro-active measures."
Mr Karr was arrested at an apartment in Bangkok.
John Mark Karr (centre) says he was with JonBenet when she died
Paraded briefly before reporters on Thursday, Mr Karr, when asked if he killed JonBenet, said: "No, I did not. It was an accident."
Mr Karr's ex-wife has since insisted he was with her during the period that the murder happened.
JonBenet's family have fought for years to clear their names of persistent accusations of involvement in the death of their daughter.
Her mother, Patsy - who died of cancer this year - had called police on 26 December 1996 to say JonBenet was missing and that there was a ransom note demanding $118,000 (£62,000).
After an initial police search of the home, officers asked her father, John Ramsey, to look again and he found JonBenet's body in the basement.