Saturday's violence comes only two weeks after the government crushed a rebel run on Damascus that included incursions by fighters into downtown neighborhoods and an audacious bomb attack that killed four members of Assad's inner circle.
The fighting in Damascus appeared likely to drain the army's resources as fighting stretches into its second week in Aleppo, 350 kilometers (215 miles) to the north.
Late Friday, Syria's official news agency SANA said government forces had hunted down the remnants of the "terrorist mercenaries" its term for the rebels in the capital's southern neighborhood of Tadamon. It said several were killed and many others wounded.
Syria's uprising began in March 2011 with mostly peaceful protests against the regime, but the conflict has transformed into a civil war. Activists say 19,000 people have been killed.
As the fighting grinds on, Syria reached out to its powerful ally Russia on Friday. Senior Syrian officials pleaded with Moscow for financial loans and supplies of oil products an indication that international sanctions are squeezing Assad's regime.
Syria is thought to be burning quickly through the $17 billion in foreign reserves that the government was believed to have at the start of Assad's crackdown.
Deputy Prime Minister Qadri Jamil, who has led a delegation of several Cabinet ministers to Moscow over the past few days, told reporters Friday that they requested a Russian loan to replenish Syria's hard currency reserves, which have been depleted by a U.S. and European Union embargo on Syrian exports.
Russia has protected Syria from U.N. sanctions and continued to supply it with weapons throughout the conflict. The Kremlin, backed by fellow veto-wielding U.N. Security Council member China, has blocked any plans that would call on Assad to step down.
On Saturday, China said the West that should be blamed for obstructing diplomatic and political efforts to restore order and peace in Syria.
Wang Kejian, a deputy director of north African and west Asian affairs at the Chinese Foreign Ministry, told a news conference that Western countries had hindered and sabotaged the political process by advocating regime change.
Wang reiterated China's stance that the solution to the Syria crisis should be a political one and that it is opposed to any military intervention.