Clashes between Syrian government forces and opposition fighters killed 14 rebels in a flare-up overnight along a strategic corridor between Damascus and the Lebanese border, activists said on Thursday.

The fighting in Zabadani a town near Damascus and the last rebel stronghold in the area is part of the larger battle for control of the mountainous Qalamoun region, stretching from the Syrian capital to the border with Lebanon.

President Bashar Assad’s forces, backed by Lebanese militant Hezbollah fighters, launched an offensive in Qalamoun in mid-November, ousting rebels from the area and cutting their supply routes from Lebanon.

According to the Britain-based Syrian Observatory for Human Rights, which gathers reports from opposition activists on the ground, the latest bout of clashes killed 14 rebels and an unknown number of soldiers. Syrian government does not publicize its casualty figures in the three-year-old conflict.

Another activist group, The Syria-based Local Coordination Committees, said government aircraft dropped four crude bombs on Zabadani overnight.

The Qalamoun region was a key supply corridor from Lebanon to opposition-held rural areas around Damascus. From there, rebels have been firing mortars into the capital, the seat of Mr. Assad’s government.

While mortar attacks have subsided since the fall of two opposition strongholds in Qalamoun, rebels are still able to strike with lethal force in the heart of the capital and other cities.

Syrian state news agency SANA said two teachers were wounded when mortar shells exploded near a school in the central Damascus district of Qanawat on Thursday. Earlier this week, a massive double car bombing in the central city of Homs and a mortar strike in Damascus killed at least 54 people.

Also on Thursday, activists said that the death toll from a government airstrike that hit a school in the northern city of Aleppo the previous day rose to 20, including 17 children.

Initially, 10 children were reported killed when a Syrian fighter jet struck the school in the city’s rebel-held eastern section. But the Observatory, which relies on reports by activists on the ground, said seven more bodies were later pulled from the rubble.

The attack took place as teachers and students were preparing an exhibit of children’s drawings depicting Syria at war, activists said. The local Aleppo Media Center put the toll at 25 killed, most of them children.

Aleppo, Syria’s largest city, has been divided between government forces and rebels for nearly two years, with constant fighting doing little to change the balance on the ground. Mr. Assad’s forces have been carrying out airstrikes and dropping crude barrel bombs in rebel-held districts in the eastern part of the city, at times hitting schools, mosques and markets.

Thousands of Syrian children have been killed in the country’s bloody conflict, which began as protests against Mr. Assad’s rule in March 2011. The revolt became an armed uprising after some opposition supporters took up arms to fight a brutal government crackdown. It turned into a civil war, which has killed more than 150,000 people and displaced millions.

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