Plumes of dark smoke could be seen rising from eastern neighborhoods.
The second wave of the assault started when a large explosion, thought to be a vehicle bomb, was reported around dawn between the districts of Jobar and Qabun, in the northeast of the capital.
"Very frightening situation for civilians living in Syria's most populous city at the moment".
The Syrian armed forces managed to stop the advancement and isolated the jihadists in the al-Mamel area in the southern al-Qaboun district, located to the north of the embattled Jobar area, repelling all attempts to break through the siege. The source said a group of rebels that had entered the area had been encircled and were "being dealt with".
Syrian state media said 15 people were wounded in rebel shelling across the capital.
The military deployed tanks along the city's leafy Fares al-Khoury Avenue leading to the eastern Jobar and Qaboun neighborhoods, where opposition forces have been pinned for years, and the cracks of gunfire could be heard from Abbassin Square.
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There was no immediate comment from the Syrian army, which said on Monday it had recaptured all the areas in northeastern Damascus lost after a surprise rebel assault on Sunday in the strategic entrance to the heart of the capital.
Syrian state media confirmed the rebels had re-entered parts of Damascus, but said the army was bombing their positions and was repelling the attack.
The SOHR said at least 143 air raids were conducted by the Syrian army on rebel held eastern parts of Damascus, mostly targeting Jobar, since the rebels launched their offensive. The militant group, which has been excluded from the all-Syrian ceasefire and recently recognized by the United States as a terrorist entity, has been joined in its push by hardline Ahrar Al-Sham as well as some factions of the Free Syrian Army. Rebels were reportedly trying to improve their standing in the peace talks with this latest ambush in Damascus.
Under such agreements, the government agrees to end bombardments and stop besieging towns in exchange for a rebel withdrawal.
With the Syrian regime regaining control of major area of the country, Syria analysts believe that government forces will begin to refocus on Damascus with the aim of taking complete control of the capital city.
The rebels had gained control over several positions in the area around Soran and in Maardas just south of it, SOHR said.