The Observatory said Monday that the government had blown up homes between the airport and the neighborhoods to establish a buffer zone.
One fighter in the area reached Monday said the government appeared set on pushing the rebels out.
"The noise from the bombardment is astounding today," said the fighter, who gave only his first name, Iyad, for security reasons. "The regime is using all kinds of weaponry."
The U.N. says that more than 60,000 people have been killed since Syria's crisis began with anti-regime protests. The conflict has since descended into civil war, with rebel brigades across the country fighting Assad's forces.
International diplomacy has failed to end the conflict.
On Monday, the secretary general of NATO said the alliance had no plans to intervene in Syria, warning that foreign intervention could have "unpredictable regional repercussions."
Anders Fogh Rasmussen told a defense conference in Sweden that Syria is more politically, religiously and ethnically complex than Libya, where NATO airstrikes in 2011 helped rebels overthrow Moammar Gadhafi.
Still, NATO is deploying Patriot missiles along Turkey's southern border with Syria to help the alliance member guard against spillover from the war.
Russian Foreign Minister Sergey Lavrov on Monday reiterated his criticism of Western calls that Assad step down.
During a visit to Ukraine, Lavrov suggested that Assad's opponents propose their own solution to the conflict.
Syria's splintered opposition has never offered a unified view on how to end the conflict or what should follow, other than agreeing on Assad's ouster.
"If I were in the opposition's place, I would put forth my own ideas in response on how to establish a dialogue," Lavrov said.
Iyad, the fighter near Damascus, said the opposition's key demand hasn't changed.
"We have said a million times we will accept nothing less than Assad's resignation," he said.
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Associated Press writers Zeina Karam in Beirut and Jim Heintz in Moscow contributed to this report.
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