At least eight people have been killed in four days of cross-border shelling which the two neighbors have blamed on each other.
With a lull in fighting since early Monday, the UN Security Council has held back from formal talks on the clashes to give time to an Indonesian mediation bid, diplomats said.
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The UN chief told reporters that he had spoken by telephone with Cambodia's Premier Hun Sen and Thai Prime Minister Abhisit Vejjajiva about the renewed clashes around the ancient temple of Preah Vihear.
Ban said he urged both "to end violence, to exercise restraint, and find a lasting solution to the dispute through established mechanisms and arrangements. The United Nations remains at their disposal to assist."
Hun Sen has called for a UN buffer force to be put on the border and for an urgent Security Council meeting on the clashes, which have left five Cambodians and three Thais dead.
In a letter sent to the United Nations on Monday, Hun Sen accused Thailand of launching "a full scale armed aggression against Cambodia, using heavy sophisticated weapons," according to a copy seen by AFP.
The Cambodian leader said that some of the Thai artillery shells "have landed as far as approximately 20 kilometers (13 miles) inside Cambodian territory," added the letter.
Hun Sen called the shelling "extremely grave aggressions by Thailand" to justify his demand for an urgent Security Council meeting.
Thailand's Foreign Minister Kasit Piromya said in his letter to the United Nations that Cambodia had set off the hostilities on Friday afternoon -- hours after he had held talks in the region with his Cambodian counterpart.
"On February 4, 2011 at 15:20 hours, Cambodian troops opened fire at a Thai military post at Phu Ma Khua in Thai territory, using heavy weapons such as mortars, rocket-propelled grenades, recoilless rifles, long range artillery and multi-launcher rockets," said the minister.
He added that on top of the deaths and about 13 wounded Thai, some 6,000 people had fled their villages on the Thai side of the border.
"While Thailand has always exercised maximum restraint, Thai soldiers had no choice but to exercise the inherent right of self-defence" under the UN charter, the minister added in the letter, which was also released to AFP.
"Thailand protests in the strongest terms against such repeated and unprovoked armed attacks by Cambodian troops, which constitutes an act of aggression," said the letter.
The Thai minister said the two sides were "engaging in close consultations" to end the dispute.
