Syrian warplanes bombarded Bazreh and in Mouadamiya, located in the western part of the city, beginning Monday, Reuters reports.
Assad's forces have refrained from new attacks and spend the past month hunkering down in anticipation of the U.S. strikes.
But President Obama's decision to delay the attacks, in order to garner congressional approval for U.S. intervention in Syria, has given regime forces a window to try and clear Damascus of rebel fighters.
Assad's alleged use of chemical weapons in August was the regime's attempt to clear rebel positions near the government's seat of power in the country, according to U.S. intelligence.
Use of those weapons crossed an administration "red line" which Obama said would trigger an armed American response.
"I think it [was] absolutely predictable," Sen. John McCainJohn McCainGOP lawmakers defend Trump military rules of engagement Senate backs Montenegro's NATO membership Senate about to enter 'nuclear option' death spiral MORE (R-Ariz.) said of the renewed offensive by Assad's forces in Damascus.
The attacks, he added, was another clear sign that Washington must reemphasize and increase its support for the Free Syrian Army (FSA), the largest and most organized block of Syria's rebel forces.
"Give them the weapons and equipment needed to prevail," said McCain, who was one of the Senate's earliest and most ardent supporters of U.S. military intervention and support in Syria.
"Right now . . . not a single weapon from the United States of America has reached the hands" of the FSA.
However, a majority of lawmakers on Capitol Hill remain opposed to any U.S. action in Syria. Congressional critics of American intervention claim military action would suck U.S. forces deeper into another war in the Mideast.
But Washington and its allies are now working a Russia-led plan to force Assad to give up his chemical weapons stockpiles to international control, led by the United Nations.
On Tuesday, Defense Secretary Chuck HagelChuck HagelSenators tear into Marines on nude photo scandal Lobbying World Who will temper Trump after he takes office? MORE said the Russia plan, proposed by Moscow on Monday, represented a "real solution" to end the U.S. standoff with Syria.
Secretary of State John KerryJohn KerryCongress, Trump need a united front to face down Iran One year ago today we declared ISIS atrocities as genocide Trump’s realism toward Iran is stabilizing force for Middle East MORE told members of the House Armed Services Committee that he plans to meet with Russian Foreign Minister Sergi Lavrov on Tuesday, to discuss the validity of the Moscow's plan.
The proposal represents a significant break for the Obama White House, given Russia's long-standing support for the Assad regime since the beginning of the civil war there.
On Monday, Obama said it would be "possible" for Syria to avert a military strike if it agrees to turn over its chemical weapons.
"It's possible if it's real," Obama told CNN in one of six network interviews he taped on Monday.
On Tuesday, Speaker John BoehnerJohn BoehnerNunes rebuffs calls for recusal Wounded Ryan faces new battle Bottom Line MORE (R-Ohio) also said he was "skeptical" that Russia would be able to convince Assad to give up his chemical weapons.
However, BoehnerJohn BoehnerNunes rebuffs calls for recusal Wounded Ryan faces new battle Bottom Line MORE said it would be up to the president to prove the viability of the Russia deal to the American people during a televised address Tuesday night.
--Story was updated at 4:00PM