It was unclear what sparked the latest clash, which lasted at least half an hour and came after a cease-fire was brokered late Friday. Tensions between the Southeast Asian nations have risen in recent days because of pressure from powerful Thai nationalist groups that have been urging Bangkok to oust Cambodians from land near Cambodia's Preah Vihear temple that they claim is actually part of Thailand.
While full-blown war is unlikely, nationalist passions are inflamed on both sides - and no clear way to settle the territorial dispute.
Gen. Chea Tara, the deputy commander of Cambodia's armed forces, said Preah Vihear temple - a U.N. World Heritage Site - was damaged when fighting began Friday. He said several mortar and artillery shells exploded just yards (meters) away, slightly marring its walls and setting grass and several trees nearby ablaze.
Casualty accounts differed, but as many as four have died in two days - one civilian each from Thailand and Cambodia, and one soldier from both nations, according to military and media reports from the two sides.
Fighting resumed Saturday morning a few miles (kilometers) away from the temple. Ath Vicheth, a Cambodian soldier in the area, told The Associated Press by telephone that it began after a group of Thai soldiers tried to cross the border in search of missing soldiers.
Thai Army Spokesman Col. Sansern Kaewkamnerd, however, denied the claim and said no Thai soldiers were missing or captured. He said a total of eight Thai soldiers have been wounded since Friday and 13 Thai homes were either burned down or damaged. One Thai soldier was killed Saturday, he said.
Thailand's Foreign Ministry said at least 3,000 people have fled their homes.
On Saturday, Cambodian troops could be seen sending trucks filled with soldiers, as well as supplies of fuel and food to the region.
Washington on Friday urged both sides "to exercise maximum restraint and take all necessary steps to reduce tensions and avoid further conflict," U.S. State Department spokesman P.J. Crowley said in a statement.
Relations between the two countries have been contentious for years, including a series of small but sometimes deadly skirmishes over the demarcation of the border near Preah Vihear.
The International Court of Justice ruled in 1962 that the temple belongs to Cambodia, but the decision rankled Thailand.
The issue was virtually dormant until Cambodia successfully applied in 2008 to UNESCO to have the temple declared a World Heritage site, an application backed by the government in power in Thailand at the time.
Thai nationalists have argued that the action threatened Thailand's sovereignty, though their protests were seen mainly as a way of rallying criticism to help oust the Thai government. Both countries' leaders, defending their patriotic credentials, then built up military forces at the border.
Last week, the nationalist group that seized Bangkok's airports two years ago gathered in the capital to pressure Thai Prime Minister Abhisit Vejjajiva over the land dispute.
The rally by the People's Alliance for Democracy - also known as the Yellow Shirts - raised tensions in a country still recovering from political violence last year in which about 90 people died.
Associated Press Writer Thanyarat Doksone contributed to this report from Bangkok, Thailand.