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"I would like to draw your attention to the explosive situation at the border," said the letter addressed to UN Security Council president Maria Luiza Ribeiro Viotti.
The letter accused Thailand of starting the fighting, but did not explicitly ask for UN intervention.
"Facing this flagrant aggression, Cambodian troops had no option but to retaliate in self-defence," it reads.
One Thai soldier was killed Saturday in renewed gunfights between the neighbouring countries near a disputed 11th-century temple, just hours after earlier skirmishes left a Cambodian soldier and a Thai civilian dead.
Thailand and Cambodia have each accused the other of triggering the clashes.