People could access the videos of the child's murder on her father's Facebook page for roughly 24 hours, until they were taken down around 5 p.m. in Bangkok on Tuesday, or about a day after being uploaded.
"This is an appalling incident and our hearts go out to the family of the victim," a Singapore-based Facebook spokesman said in an email to Reuters. "There is absolutely no place for content of this kind on Facebook and it has now been removed."
Murders, suicides and sexual assault have plagued Facebook despite making up a small percentage of videos. On Tuesday a Swedish court jailed three men for the rape of a woman that was broadcast live on Facebook.
Last week, Facebook said it was reviewing how it monitored violent footage and other objectionable material after a posting of the fatal shooting of a man in Cleveland, Ohio was visible for two hours before being taken down.
The harrowing footage from Thailand showed Wuttisan Wongtalay tying a rope to his daughter Natalie's neck before dropping the child, dressed in a bright pink dress, from the rooftop of a deserted building in the seaside town of Phuket.
Wuttisan's suicide was not broadcast but his lifeless body was found beside his daughter, said Jullaus Suvannin, the police officer in charge of the case.
"He was having paranoia about his wife leaving him and not loving him," Jullaus told Reuters.
Wuttisan's wife, Jiranuch Triratana, told Reuters she had lived with him for over a year. At first the relationship had gone well, she said, but then he grew violent and sometimes hit her 5-year-old son from a previous husband.
She feared that something was wrong on Tuesday when she found he had left home with Natalie, whose nickname was Beta. She set out to look for them.
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"I was afraid he would hurt our daughter even though he loved her," she told Reuters by phone from the funeral.
Thailand's Ministry of Digital Economy said it contacted Facebook on Tuesday afternoon about removing the videos, after receiving a police request.
"We contacted Facebook today and Facebook removed the videos," ministry spokesman Somsak Khaosuwan told Reuters, adding that the government would take no action against the company.
"We will not be able to press charges against Facebook, because Facebook is the service provider and they acted according to their protocol when we sent our request. They cooperated very well."
After the company faced a backlash for showing the video of the Cleveland killing, Chief Executive Officer Mark Zuckerberg said Facebook would do all it could to prevent such content in the future.
Thai netizens voiced outrage about the clips of the child's killing, which were uploaded on Monday, the first at 4.50 p.m. (0950 GMT) and the second at 4.57 p.m. (0957 GMT).
"This is the most evil clip I've seen in my life," said one user, Avada Teeraponkoon. "I couldn't stand it for more than one second."
"How can he watch his own child stop breathing?" said another, Rujirek Polglang. "He should have just died alone."
The killing was the first in Thailand known to be broadcast on the social networking site, said deputy police spokesman Kissana Phathanacharoen.
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