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.
Syrian rebels stormed a government-held area in northeastern Damascus for the second time in three days, sources on both sides said, pressing the boldest assault on the capital by opposition fighters in several years.
However, Faylaq al-Rahman, one of the rebel groups taking part in the Damascus fighting, issued a statement Monday saying the attack was ongoing in the capital.
A security government source, who requested anonymity, told dpa that the attack started with two auto bombings around 500 meters from the eastern edge of Damascus.
The attackers utilized numerous guerilla warfare techniques, including vehicle bombs, suicide attacks and the use of secret tunnels.
Russian Federation - which is conducting its own bombing campaign in Syria in support of President Bashar al-Assad - said earlier this month that more than 180 of its troops have started demining around Palmyra's ancient monuments.
Russia's foreign ministry yesterday summoned Israel's ambassador over air strikes close to Moscow's forces near the historic Syrian city of Palmyra.
A rebel commander said the Syrian army was intensifying its shelling on areas where they had advanced in Jobar and towns across Eastern Ghouta.
This footage was shared on the Failaq al-Rahman YouTube account and is described as showing the "first moments" of an attack on east Damascus. He did not have an immediate toll for Monday morning's air strikes.
Assad was quoted in comments translated into Russian that "any military operation in Syria that does not have the consent of the Syrian government is illegal".
Several rounds of peace talks so far have failed to bring about a solution to Syria's war, which entered its seventh year last week.
The YPG makes up the bulk of the Syrian Democratic Forces, a US-backed alliance of Kurdish and Arab fighters that has seized swathes of territory from the Islamic State group.
"Some (Kurds) are working with us through the Syrian Democratic Forces to fight ISIS (IS), some are not. It shows also that this new combination led by [Tahrir al-Sham] is very potent", Landis said.