The state news agency, SANA, reported that 10 people at the school, 9 students and a teacher, were killed by a mortar shell fired by “terrorists,” its term for its opponents, in Bteeha, a small town north of Damascus on the road to the central city of Homs. Antigovernment activist groups confirmed the attack, but put the death toll at nine. The road to Homs and on to the commercial hub of Aleppo has been strongly contested in recent fighting.

The Local Coordination Committees, a network of rebel groups, reported the mortar attack without comment, implying that it was carried out by the government. But an activist reached in Damascus said it was unclear who had fired the shell. Recent bombs and mortar attacks by rebels that have killed civilians have angered both supporters and opponents of the government, as even some who support the rebels express concern that the violence has spiraled out of control.

An activist in the Damascus suburbs who gave only her first name, Leena, said that activists were surprised there was an attack in Bteeha, which is usually very calm, and that information had been hard to come by because very few activist reporters were in Bteeha. She said that many residents were refugees who fled the Golan Heights in 1967 when Israel occupied the territory, and that displaced people, mostly from the Sunni Muslim sect that makes up the bulk of the Syrian uprising, have recently moved there.

“Many Golani people are actually with the revolution, and they even have their own brigades in the Free Syrian Army,” she added, referring to the loose-knit rebel umbrella group.

There were more signs of concern on the diplomatic front as well on Tuesday.

At a meeting in Brussels, NATO ministers expressed “grave” concern about reports that the Syrian government might be getting ready to use its chemical weapons. The remarks followed a warning on Monday by President Obama telling Syria not to use chemical weapons against its own people and vowing to hold accountable anyone who did, even as American intelligence officials picked up signs that such arms might be deployed in the fighting there.

“Any such action would be completely unacceptable and a clear breach of international law,” the NATO secretary general, Anders Fogh Rasmussen, said at a news conference.

In another reflection of how the conflict in Syria is spilling over its borders, NATO agreed to deploy Patriot surface-to-air missiles in Turkey, which had requested the installations as a defense against cross-border violence.

More evidence emerged on Tuesday that the situation in Syria was deteriorating, a day after the United Nations and the European Union announced they were curtailing activities and pulling staff members out of Damascus, the capital. The United Nations World Food Program, which is feeding 1.5 million people in Syria, 85 percent of them displaced by the fighting, issued a report warning that food shortages were intensifying because of rising bread prices and indiscriminate attacks on United Nations vehicles that made food distribution difficult.

The roads are so dangerous, the agency said, that it is trying to obtain more armored vehicles to allow its provincial offices to continue to monitor food distribution.

The agency, along with other United Nations organizations, has suspended its operations outside Damascus and sent home nonessential foreign staff members, further hampering its work, it said. Most food distribution is done by local partners, mainly the Syrian Arab Red Cross. Still, the World Food Program maintains 20 foreign and 100 local employees in Syria.

“I can absolutely confirm to you that we will continue our work,” Muhannad Hadi, the country director, said in an interview from Jordan, where he had traveled on business with plans to return to Syria.

Food shortages are increasing, especially in Aleppo, where bread prices are 50 percent higher than in the rest of the country, the agency statement said, adding, “Food consumption is particularly low among displaced families taking refuge in schools and public buildings, due to the lack of access to cooking facilities.”

Rebels and government forces continued to clash around a strategic air base at Wadi al-Deif, near Maarat al-Noaman, a crossroads town on the road between Damascus and Aleppo, as government airstrikes around Damascus continued for a fourth day with no sign of abating and neither side apparently able to win.

Even as the government was bringing extreme force to bear, it was still unable to quell the rebels, who have managed to disrupt the airport and force a counteroffensive to seal off the city center from the restive suburbs. Yet although rebels have managed to put pressure on the government around Damascus in recent weeks, several fighters interviewed said that the battle had become exhausting and that there was no coordinated strategy.