According to a Syrian military source, the army had managed to recapture all the positions lost in Sunday's attack. "The government and allied forces have retaken the initiative and are striking the groups that launched yesterday's assault".
Abdel Rahman said it was unclear whether government forces or their Russian allies were carrying out Monday's raids on Jobar.
Qaboun and Arbin, to the north and north-east, were also under attack, it said.
It was a surprising breach of Damascus' security perimeter, where the government has effectively walled itself off from opposition forces encamped in two enclaves in the eastern parts of the city.
Control of Jobar is divided between the government and rebel factions.
The rebels began the day with two auto bombs and several suicide attacks, the British-based Syrian Observatory for Human Rights monitoring group reported.
The rebel offensive was launched in the Jobar district of eastern Damascus, and was led by Islamist groups including Ahrar al-Sham and the recently formed umbrella jihadist group Hayat Tahrir al-Sham. It aired footage from Abbasid Square, typically buzzing with activity but now empty except for the sound of shelling.
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Jabhat Fateh al-Sham was formerly known as al-Nusra Front before purportedly breaking away from the outfit, which operated as al-Qaeda's Syria branch.
"These are not intermittent clashes - these are ongoing attempts to advance", he said.
The attack on Damascus comes just days before a fresh round of UN-brokered peace talks in Geneva aiming to put an end to Syria's six-year war.
The intensity of the Syrian army's counterattack forced the rebels to retreat on Sunday night from at least 60 percent of the areas they captured that day in an industrial area that separated Qaboun from Jobar, a rebel spokesman said.
"After a major advance by opposition fighters, the regime got over its shock and began a counter-offensive", he said.
The government has been trying to pressure the rebels to surrender the pockets they hold in Damascus, following victories in the northern city of Aleppo, the central city of Homs and other Damascus suburbs.
It has undertaken a relentless bombing campaign of residential areas to force rebels to surrender and agree to deals that push them out of these areas.