The fiercest border clashes in years also damaged a landmark 11th century temple near a strip of disputed land that Thai nationalists have seized on as a domestic political issue.
There are conflicting casualty tolls, but as many as four have died in two days - one civilian each from Thailand and Cambodia, and one soldier from each nation, according to officials from the two countries. Each side blames the other for starting the fighting.
Tensions between the Southeast Asian nations have risen in recent days because of demonstrations by influential Thai nationalist groups in Bangkok demanding that the government oust Cambodians from land near the 11th century Preah Vihear temple. The nationalists claim the land is actually part of Thailand.
The demonstrators - from the same group, the People's Alliance for Democracy, that in 2008 occupied the Thai prime minister's offices and Bangkok's two airports in a bid to force out two previous governments - have said they will escalate their pressure on Thai Prime Minister Abhisit Vejjajiva.
The rally by the PAD - also known as the Yellow Shirts - has raised tensions in a country still recovering from political violence last year in which about 90 people died.
While full-blown war is unlikely, nationalist passions are inflamed in both countries - with no clear way to settle the long-standing territorial dispute surrounding the temple, built during a time when Cambodia's Khmer empire ruled over much of Thailand.
Thai Army Spokesman Col. Sansern Kaewkamnerd said 2nd Region Army Commander Lt. Gen. Tawatchai Samutsakhon met with Cambodian generals after Saturday's fighting to agree on a cease-fire and not to deploy more troops to the area.
The two sides also agreed that Thailand would suspend construction of a road to the disputed area, which covers just 1.8 square miles (4.6 sq km), according to the private Cambodian Television Network, which is close to the government.
"Everything depends on the Thai side. New fighting will erupt if Thai soldiers enter our territory, but there will be no fighting if they do not enter," Cambodian Maj. Gen. Srey Doek told reporters after the meeting.
The latest round of fighting began Friday on land near Preah Vihear temple, a U.N. World Heritage site that belongs to Cambodia under a 1962 World Court ruling disputed by many Thais.
Several mortar and artillery shells exploded just yards (meters) away from Preah Vihear, slightly damaging its walls and setting grass and several trees nearby ablaze, said Gen. Chea Tara, the deputy commander of Cambodia's armed forces.
Thailand's Foreign Ministry said at least 3,000 people have fled their homes, while Sar Thavy, deputy governor of Cambodia's Preah Vihear province, said 1,000 families had been evacuated.
Thailand initially said the flare-up could have been caused by a misunderstanding, but Cambodia described it as a deliberate "Thai invasion," claiming that as many as 300 Thai soldiers advanced Friday on a small pagoda to try to take down the Cambodian flag.
Ath Vicheth, a Cambodian soldier in the area, told The Associated Press by telephone that Saturday's 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 eight Thai soldiers have been wounded since Friday and 13 homes were either burned down or damaged. One Thai soldier was killed Saturday, he said.
The Preah Vihear 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.
___
Associated Press Writer Thanyarat Doksone contributed to this report from Bangkok, Thailand.