Assad's powerful brother-in-law, his defence minister and a top general were killed in Wednesday's attack. The head of intelligence and the interior minister were wounded.
Government forces have responded by blasting at rebels in their own capital with helicopter gunships and artillery stationed in the mountains overlooking it.
Assad's failure to appear in public for more than 24 hours - he was finally shown on television on Thursday swearing in a replacement for his slain defence minister - added to the sense of his power evaporating. His whereabouts are not clear.
Diplomatic efforts - rapidly overtaken by events on the ground - collapsed in disarray on Thursday when Russia and China vetoed a U.N. Security Council resolution that would have imposed sanctions unless Syrian authorities halted violence. Washington said the council had "failed utterly."
Activists in Damascus said rebels were now in control of the capital's northern Barzeh district, where troops and armoured vehicles had pulled out.
The army had also pulled out of the towns of Tel and Dumair north of Damascus after taking heavy losses, they said. But they said troops were hitting the western district of Mezzeh with heavy machineguns and anti-aircraft guns overnight.
The reports could not be confirmed. The Syrian government restricts access by international journalists.
A resident who toured much of Damascus late on Thursday said he saw signs the government's presence was diminishing, with only sporadic checkpoints and tanks in place in some areas. The Interior Ministry at the main Marjeh Square had a fraction of its usual contingent of guards still in place.
Shelling could be heard on the southwestern suburb of Mouadamiyeh from hills overlooking the city where the Fourth Division, commanded by Assad's brother Maher, is based, he said.