The Scot, named as 36-year-old Gareth Crowe, was said to have been thrown by the animal after it turned on its handler during an outing on Koh Samui.
The Bangkok Post said he was trampled on by the elephant and stabbed in the torso by its tusk on Monday afternoon.
It is understood his teenage daughter Eilidh escaped with minor injuries and is being treated in hospital.
His partner Catherine Hughes and their son were not on the trek, according to reports which also suggested the elephant named Golf was upset before the incident in the Tambon Bor Phud area and was not responding to its handler’s commands.
Mr Crowe’s daughter appeared to respond to witness claims her father had teased the animal with a banana.
Eilidh Hughes wrote on the Samui Times website: “He was not teasing the elephant as I was his 16-year-old daughter who is lying in hospital and I was on it.”
The charity World Animal Protection said its thoughts were with the man’s loved ones but the incident was a “stark reminder” that elephants are not meant to be ridden.
A spokeswoman said: “Elephants are cruelly abused to tame them enough so they give rides and perform in shows.
“Most tourists don’t know about these abuses or the potential danger they put themselves in.
“If you can ride it, hug it or have a selfie with a wild animal, then the chances are it is cruel and the animal is suffering.”
A spokesman for the Foreign and Commonwealth Office said: “We are offering support to the family of a British national who has sadly died following an incident in Koh Samui, Thailand, and are making contact with the local authorities to seek further information.”
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