(CNN) -- The chairman of the Association of Southeast Asian Nations on Tuesday pushed for talks between Thailand and Cambodia to end deadly clashes that have erupted over a temple along the border.
The issue "can only be addressed bilaterally," said Marty M. Natalegawa, who is also the Indonesian foreign minister. He added that he has the impression, after visiting Phnom Penh and Bangkok, that there is an overwhelming commitment on both sides to "address their issues through peaceful means, through dialogues and negotiations."
The border skirmishes, which started Friday, have killed five people, including members of the military and civilians, a statement from ASEAN said, adding that each nation accuses the other of firing first.
Thailand's official news agency, MCOT, reported Tuesday, "Since the fighting erupted Friday, one Thai soldier was killed, 25 were wounded and one civilian died in the clashes."
The report added that Cambodia on Tuesday "handed over a Thai soldier captured during the cross border clash."
Cambodia's official news agency, AKP, reported Tuesday that "Cambodian Prime Minister Samdech Akka Moha Sena Padei Techo Hun Sen has sought the United Nations' intervention in arranging a buffer zone" at the border area and wants to make sure the fighting does not expand to other parts of the border.
The U.N. Security Council on Monday expressed "grave concern at aggravation of tensions between Cambodia and Thailand" and said it was willing to hold an emergency meeting requested by Cambodia, but first wanted to wait for regional mediation efforts by the Indonesian foreign minister.
An official Thai report said the two sides had agreed to a ceasefire on Saturday, but skirmishes continued after.
The clashes stem from a longstanding conflict related to the 11th-century Preah Vihear temple. The building sits on a cliff in Cambodian territory, but the most accessible entrance to the site is on the Thai side.
In a letter to the United Nations over the weekend, Cambodian Prime Minister Hun Sen said that in addition to the human toll the fighting was taking, the temple had suffered damage.
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 the 1.8-square mile (4.7-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, meaning the U.N. believes the place has outstanding universal value.