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Air strikes were reported in the town of Mleha, where a suicide bomber detonated himself at a checkpoint on Saturday.
Yasser al-Abboud, a senior rebel commander, was killed in southern Syria, according to state media and activists.
Abboud, who defected from the Syrian army, reportedly died while leading an assault in Tafas, according to the BBC. He headed the operations room in Deraa province for the opposition Supreme Military Council.
While state media labeled Abboud a "criminal, treacherous... deserter," an activist told Agence France-Presse that he was "one of the most effective commanders on the ground."
Syrian warplanes struck southeast of Damascus on Monday after rebel forces made advances in the area.
Meanwhile, air strikes were reported in the town of Mleha, where a suicide bomber detonated himself at a government checkpoint on Saturday.
Rebels later took the checkpoint and set up positions in a burned out pharmaceutical factory.
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The rebel-held Damascus suburb of Moadamiyeh is facing extreme difficulties getting food, according to the Associated Press.
Heavy fighting in the area forced more than 3,000 residents to flee their homes, but many remain trapped.
Forces loyal to the Syrian government have reportedly laid siege to the area in an attempt to starve out the rebels.
Residents of the neighborhood signed an open letter distributed by an anti-government group, which plead for help from the international community.
"Save us from death. Save us from the hell of Assad's killing machine," the letter said.
"For nearly one year, the city of Moadamiyeh has been under siege with no access to food, electricity, medicine, communications, and fuel."
The Syrian civil war, now well into its second year, has killed more than 100,000 people and made more than 2 million refugees, according to UN estimates.
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