UN Secretary-General Ban Ki-moon on Saturday called for a ceasefire and said the neighbours should launch "serious dialogue" to resolve the dispute.
Thousands of civilians have fled both sides of the disputed jungle frontier because of the fighting, which has shattered a tense two-month lull in hostilities.
Sixteen camps in the area are providing refuge to more than 18,000 people, who have fled the fighting which has ended two months of calm, and the number was expected to rise to 20,000 by Sunday evening, Thai officials said.
Cambodian officials said 12,000 people had been evacuated.
The latest clashes have taken place near a different group of temples more than 100 kilometres away from the Preah Vihear temple which has been the focus of a long-running dispute which last blew up in February.
Both countries have accused each other of sparking the violence.
On Sunday Thai Prime Minister Abhisit Vejjajiva said his country was willing to hold bilateral talks and accused Cambodia of trying to "internationalise" the conflict by asking for outside mediation.
Indonesian Foreign Minister Marty Natalegawa is expected to travel to both countries on Monday for talks on the conflict. Jakarta, which holds the rotating chairmanship of the Association of South-East Asian Nations (Asean) regional bloc, has called for an immediate end to the violence.
The neighbours agreed in late February to allow Indonesian observers near Preah Vihear, but the Thai military has since said they are not welcome.