The four dead spanned three generations, including an 85- year-old grandmother and her 39-year-old granddaughter, according to the The Star newspaper.
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"We are all in shock," a relative of the family in Malaysia told the paper.
Some 22 Malaysians, mostly elderly, had gone to Chiang Mai on December 17 for a five-day tour organised by Malaysian operator Chiu Travel.
The accident occurred on Sunday in Doi Saket district 30 kilometres (18 miles) from the northern city of Chiang Mai.
Images posted online by local news outlets showed scene of devastation as rescuers battled to reach those trapped inside the smashed bus, which had come to rest in thick foliage with its roof caved in.
In one picture white sheeting had been draped over victims' remains.
Chiu Travel manager Terence Yung told AFP that the company had flown 15 Malaysian relatives of victims to Thailand and they were expected to reach Chiang Mai Monday evening to help identify bodies.
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Thai police said a total of 14 people were killed in the accident, 13 Malaysians and one Thai. Malaysia's foreign ministry and Chiu Travel confirmed the number of Malaysians killed in the crash as 13. Chiu Travel said one Thai tour guide had died as well.
The Malaysian foreign ministry said in a statement Monday that four Malaysians were severely injured while another five sustained injuries which are "not life threatening".
Yung said his company was still trying to find out how the accident happened but said, based on information he had received from Thailand, the crash was a result of the driver trying to overtake another vehicle.
"The only way we can stop these accidents is for the tour leader to ensure the local (Thai) drivers don't drive recklessly," he said.
Prime Minister Najib Razak expressed sadness on his Facebook page.
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"I am saddened to hear news of the accident in Chiang Mai where 13 Malaysians died and express my condolences to the victims' families," he wrote.
"The government would ensure every effort is made in bringing home the victims' bodies and help the victims' families."
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