The government's response has been harsh, and suburbs to the east and south of Damascus have seen some of the heaviest fighting since July, when rebels seized neighborhoods in the capital itself before being routed by government troops.
Death tolls in the area have soared. On Tuesday, reports emerged of at least four killings of at least a dozen people, all of them near Damascus or in Aleppo, Syria's largest city and a battleground since the summer.
Syria's state news agency SANA said nine students and one teacher were killed when a mortar fired by "terrorists" — the regime's shorthand for rebels — hit a ninth grade classroom in the Al-Wafideen area. The housing project, about 25 kilometers (15 miles) northeast of central Damascus, houses 25,000 people displaced from the Golan Heights since the 1967 war between Syria and Israel.
SANA said earlier that 29 students and one teacher had been killed before reporting the lower number.
The opposition Syrian Observatory for Human Rights said 10 were killed and did not specify who fired the mortar.
The Britain-based group, which relies on contacts inside Syria, also said 17 unidentified bodies were found in the southern Damascus suburb of Thiyabiyeh. An activist video posted online showed the dead lined up on a floor, many of their heads bloody. An off-camera voice said they were shot after being detained at government checkpoints.
The Observatory also said 12 others were killed in a shelling attack on the Aleppo neighborhood of Bustan al-Qasr the day before. Online videos showed bloody and dismembered bodies on a sidewalk as people struggled to lift the wounded
Nearby, dozens of men stood in what the unidentified cameraman said was a bread line.
"We still see people standing in a long line despite a massacre to get bread," the cameraman says.
The Observatory also reported 13 dead in a separate attack Monday in Aleppo's Halak neighborhood.
The videos appeared genuine and corresponded to other reports on the incidents. Syria's government severely restricts media access, making independent confirmation nearly impossible.
Syria's uprising began with peaceful protests in March 2011 and later escalated into a civil war that the opposition says has killed more than 40,000 people. So far, both sides have refused international calls for a negotiated solution.
Most analysts agree that the tide is turning, however slowly, against the regime.
But Fyodor Lukyanov, editor of the foreign policy magazine Russia in Global Affairs, said Assad won't leave without a fight.
"Assad realizes that there is no way back for him," said Lukyanov, a leading Russian foreign policy expert with high-level Foreign Ministry connections. "If he tries to jump the boat, his own supporters will not forgive him for doing that. And if he loses, no one will give him any guarantees."
Associated Press writers Albert Aji in Damascus, Syria, Barbara Surk in Beirut, Ian Deitch in Jerusalem, Slobodan Lekic in Brussels and Kimberly Dozier and Pauline Jelinek in Washington contributed to this report.