(CNN) -- Fighting between Thai and Cambodian troops flared again briefly on Saturday morning, after clashes over an ancient temple claimed by both countries erupted along the border on Friday.
A Thai Army spokesman said one soldier was killed in the latest round of gunfire, and four others were injured. That brings the weekend death toll to two people. Earlier, the country's health minister told the MCOT news agency that one Thai villager was killed by artillery shells fired by Cambodian troops.
Fighting took place on Friday and Saturday near the Preah Vihear temple, an 11th century structure which straddles the boundary between Cambodia and Thailand. The building itself sits on a cliff in Cambodian territory, but the most accessible entrance to the site is on the Thai side.
State media for both countries confirm that there was an exchange of gunfire and artillery on Friday afternoon for about two hours. Both sides are pointing the finger at the other over who fired the first shots.
The United States urged Thailand and Cambodia on Friday to show "maximum restraint" in the wake of clashes over an ancient temple claimed by both countries. Events along the Thai-Cambodia border were being closely monitored, according to State Department spokesman P.J. Crowley, and both sides were called on to "take all necessary steps to reduce tensions and avoid further conflict."
Conflict over the Preah Vihear site has taken place periodically for years. In 1962, the International Court of Justice in The Hague, Netherlands, ruled that the site was in Cambodia, adding that the structure was "an outstanding masterpiece of Khmer architecture."
But Thailand says that the 1.8 square mile (4.6 square kilometer) area around Preah Vihear was never fully demarcated, and blames a map drawn at the beginning of the 20th century during the French occupation of Cambodia.
In July 2008, the United Nations approved Cambodia's application to have the temple listed as a World Heritage Site -- a place the U.N. believes has outstanding universal value.