(CNN) -- Fighting flared for a third straight day Sunday along the Thai-Cambodian border over a disputed ancient temple despite a reported ceasefire and international efforts to soothe tensions.
At least seven people -- two villagers and five soldiers -- were wounded after a new gunfight broke out shortly before 7 p.m. Sunday evening, Thai Army spokesman Col. Sansern Kaewkamnerd told his nation's state-run MCOT media outlet.
The skirmish came a day after the two sides agreed to a ceasefire, according to the official Thai report.
Earlier, Thai Army Lt. Gen. Thawatchai Samutsakorn told MCOT that the situation along the border was returning to normal Sunday.
Several shops in the Kantharalak district reopened earlier Sunday, and some villagers had gone back to their homes -- though the later report noted that residents were evacuated again to temporary bunkers. Twenty schools planned to remain shuttered through at least Wednesday on the government's orders.
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.
Gunfire erupted Friday near the site, followed by more skirmishes Saturday. A Thai Army spokesman said one soldier was killed Saturday, and four others were injured. Earlier, the country's health minister told the MCOT news agency that one Thai villager was killed by artillery shells fired by Cambodian troops.
A Cambodian official, who was not named, said 10 of its soldiers and civilians were killed or injured in Friday and Saturday fighting, state-run Cambodian news outlet AKP reported. The official said Cambodian authorities had also captured five Thai troops, including four on Friday.
The United Nations weighed in on the dispute Sunday, with a statement from Secretary-General Ban Ki-moon's press office saying he is "deeply concerned" by the clashes. The world body's leader urged discussion over military confrontations, in "a spirit of dialogue and good neighborly relations."
"The Secretary-General appeals to both sides to put in place effective arrangements for cessation of hostilities and to exercise maximum restraint," the U.N. statement said. "The United Nations remains at their disposal to assist in these peaceful efforts."
On Saturday, Cambodia had formally complained in a letter to the U.N. about what it described as "intense shelling" with mortar rounds Saturday morning following an alleged armed incursion by Thai troops on Friday, according to state-run AKP news.
In the letter, Cambodian Prime Minister Hun Sen pointed to the "explosive situation at the border," alleging that 300 Thai troops on Friday "entered Cambodian territory and attacked Cambodian troops at three locations" about 500 meters (a third of a mile) from the temple. The letter also alludes to similar "acts of aggression" in 2008 and 2009 by Thai forces.
Besides the human toll, the letter claimed that the temple itself had suffered damage in the shelling and firefights.
"Facing this flagrant aggression, Cambodian troops had no option but to retaliate in self-defense in order to safeguard Cambodia's sovereignty and territorial integrity," the letter states.
The recent Thai military actions violate the 1991 Paris Peace Accord, U.N. Charter and a 1962 judgment from the International Court of Justice, the letter claims.
Thai Prime Minister Abhist Vejjajiva denied that his nation's troops had attacked Cambodian forces, telling reporters they only acted in self-defense to protect their homeland's own sovereignty, according to MCOT. That report indicated Thailand, too, had sent a letter to the United Nations about the situation.
On Sunday, the Thai leader tried to downplay the need for outside intervention to resolve the dispute, including an offer from ASEAN Secretary-General Surin Pitsuwan -- Thailand's former foreign minister and now head of the southeast Asian alliance -- to mediate.
The United States urged Thailand and Cambodia on Friday to show "maximum restraint." Events 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 -- meaning the U.N. believes the place has outstanding universal value.