The rebel soldiers appear to be getting themselves organized as they captured a few suburban neighborhoods close to the capitol city of Damascus.
President Assad reacted by sending 2,000 troops armed with tanks and artillery into the residential areas to take back control.
An activist said the Free Syrian Army - a force of military defectors with links to Syria's divided political opposition - mounted scattered attacks on government troops who advanced through the district of Saqba, held by rebels just days ago.
"Street fighting has been raging since dawn," he said, adding tanks were moving through a central avenue of the neighborhood. "The sound of gunfire is everywhere."
Russia's Foreign Ministry said Syria agreed to Russian-brokered negotiations over the crisis, but senior members of the council that claims to speak for a fragmented Syria opposition said there was no point in talking to Assad, who must quit.
"We rejected the Russian proposal because they wanted us to talk with the regime while it continues the killings, the torture, the imprisonment," Walid al-Bunni, foreign affairs chief for the Syrian National Council, told Reuters.
The rebels said at least 15 people had been killed as they pulled back in Saqba and Kfar Batna. Activists have claimed a death toll of several dozen in three days of fighting in the districts, which have seen repeated protests against Assad's rule and crackdowns by troops on the 10-month-old uprising.
It's not clear how many defectors are actually joining the FSA. The number of soldiers leaving the army is several dozen a day, according to one source. But not all defectors end up fighting the Assad regime.
The FSA claims 40,000 troops but that is almost certainly an overstatement of its strength. The numbers they can put in the field are considerably smaller, and they have no heavy weapons or much organization either.
Decisions whether to arm the FSA or not will no doubt become more pressing in the near future. The coalition of secular opposition members are adamant against doing so, fearing they would be trading one military dictatorship for another. The opposition wants a negotiated settlement with a caretaker government and Assad in exile. That will probably never happen as long as the dictator is still alive.