Prime Minister Paetongtarn Shinawatra and Deputy Prime Minister and Defense Minister Phumtham Wechayachai warned that rising tensions could hurt Thailand's economy and its border trade with Cambodia.
The Thai government said Cambodia was also worried the conflict could harm economic cooperation and disrupt trade.
A meeting of the Thai-Cambodian Joint Boundary Committee (JBC) is scheduled for mid-June to address the ongoing dispute.
Thai and Cambodian soldiers were in a stand-off last Wednesday after a brief exchange of gunfire in a border area between Ubon Ratchathani province of Thailand and Preah Vihear province of Cambodia early that morning. One Cambodian soldier was killed in the exchange, the defence ministry in Phnom Penh said.