Our correspondent, Darin Fazil, said on Wednesday that the government troops also blocked one of the main routes for supplying arms and equipment to the militants in the Rif Dimashq governorate.
She added that fierce clashes are underway between the army and the militants in Jobar.
Several government and public buildings are now under the control of the army, the report added.
Many corpses burned by the terrorists have been found on the streets of the district.
The development came a day after the Syrian army inflicted heavy losses on terrorists in the city of Homs, attacking them with artillery and air strikes for the fourth straight day.
Syrian state TV said on Tuesday that the army, using fighter aircraft, tanks and mortar units, had achieved a great success in Homs and killed a large number of terrorists.
The operation follows gains in Homs province by the Syrian troops in recent weeks.
The army established control over the strategically important town of Qusayr, between Homs and the Lebanese border, in early June. Syrian troops were backed by forces from the Lebanese resistance movement Hezbollah during the Qusayr operation.
The Syrian army’s push against the militants rattled their sponsors.
The Syria crisis began in March 2011, and thousands of people, including large numbers of government forces, have been killed.
Damascus says the chaos is being orchestrated from outside the country, and there are reports that a very large number of the militants are foreign nationals.
The Syrian government says the West and its regional allies -- especially Qatar, Saudi Arabia, and Turkey -- are supporting the militants.
In addition, several international human rights organizations say the militants operating in Syria have committed war crimes.