The official Syrian Arab News Agency said initial reports indicated students were killed and injured at the school Thursday when two shells landed, although it provided no further information.
Meanwhile, two Syrians were killed and another injured when a minibus was fired upon near Jdaidat Artouz, a Damascus suburb, SANA said.
The news agency said terrorists were behind both incidents. "Terrorists" is used by President Bashar Assad's government to describe opposition and anti-government forces.
The United Nations, meanwhile, said it was investigating reports to determine whether Turkey expelled hundreds of refugees involved in rioting Wednesday violating international asylum laws, The Guardian reported.
Sybella Wilkes, a spokeswoman for the U.N. High Commission for Refugees, said the U.N. entity has contacted the Turkish government about the reports.
"We are very concerned that there are allegations of possible deportations from the camp in the past day," Wilkes told The Guardian. "That would be a breach of international law. It would violate the principle of non-refoulement [not forcing refugees to return to their homeland if it endangered their lives], because with the situation in Syria people's lives could be in danger."
A Turkish official denied that those involved in the rioting were deported, The Daily Hurriyet in Ankara reported.
"We refute the deportation claims; nearly 500 people return every day to Syria of their own free will," the official said. "The status we provide for Syrian refugees is temporary protection; without their will, not a single Syrian national can be sent back."
The agency announced earlier this month the number of refugees topped 1 million people, and the number is rapidly increasing, Wilkes said.
"In March alone we have had an average of 10,000 people crossing per day. In February it was 8,000. In January it was 5,000," she told The Guardian. "The numbers keep going up and up."