The army's advance involved heavy fighting and intense air strikes, the Syrian Observatory for Human Rights and a military media unit run by the army's ally Hezbollah said.
State television, quoting a military source, said the army "tightened the noose around terrorist groups besieged in the industrial zone on the northern edges of Jobar". "The government and allied forces have retaken the initiative and are striking the groups that launched yesterday's assault".
The Observatory said the rebels had initiated the attack to relieve pressure on fighters under attack from government forces in the districts of Barzeh, Tishreen and Qabun.
Tahrir al-Sham - an umbrella group of rebels formed by Jabhat Fateh al-Sham last month - and the independent Failaq al-Rahman group also participated in the attack.
The sudden rebel seizure of territory in the Syrian capital - and the manner in which the attack that took place overnight and into Sunday, with rebels sneaking into the city through underground tunnels and using vehicle bombs - reflected the insurgents' most serious infiltration into Damascus in years.
Control of Jobar has been divided between moderate rebels, government troops, and jihadists for more than two years.
The incursion into Abbasid Square, though brief, was the first time in approximately two years that rebels had got that close to the heart of Damascus.
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The terrorists and their allies started advancing from the Eastern Ghouta District near the capital early Sunday after which government forces engaged them in the suburban Jobar District later in the day.
Insurgent groups attacked government positions in the area, including with two auto bombs, in an attempt to storm their defence lines, the Britain-based Observatory said. It aired footage from Abbasid Square, typically buzzing with activity but now empty except for the sound of shelling.
Air raids were also reported in neighbouring Qaboun and Arbin.
The fighting comes only days before another round of UN-brokered peace talks in Geneva aimed at finding a political solution to Syria's six-year civil war.
The Observatory said fighting was still underway Monday.
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.