Four other Thai soldiers have been killed since the fighting started on Friday, according to Col. Sansern Kaewkumnerd.
Authorities have evacuated thousands of people from nearby villages.
Each side blames the other for the violence, which first broke out last week near two temples in the Phanom Dong Rak district of Thailand's Surin province.
Cambodia's government has said three of its troops have been killed.
On Monday, Sansern accused Cambodians of trying to seize two ancient temples, Ta Kwai and Ta Muen Thom.
The fighting on the ground has been coupled by a war of words in recent days. (read more)