"Army units advanced on several fronts and retook control of several farms and villages", the source told SANA, as the regime pushed forward a devastating ground and air assault on the region.
The clashes between regime forces and rebels come after Russian Federation on Tuesday started a daily five-hour "humanitarian pause".
The regime's ground and air attacks continued on civilians in the opposition-hold area near capital Damascus despite decisions to implement a ceasefire made separately by Russian Federation and the UN Security Council.
Advances by Assad regime forces into opposition-held eastern Ghouta are causing many people to flee, a pro-Syrian opposition television station and a witness in the enclave said Sunday.
At least 21 civilians were killed by Bashar al-Assad regime forces in besieged Eastern Ghouta region.
Thousands of civilians, estimated between 300 and 400 families, took cover and fled government forces by hiding in underground shelters, the Syrian Observatory for Human Rights stated, according to Reuters.
May's office said the two agreed that "Russia and others with influence over the Syrian regime must act now to cease their campaign of violence and to protect civilians".
Orient TV said advances by forces loyal to the Assad regime had triggered wide scale displacement.
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Following decision, Turkey's ambassador to Prague , Ahmet Necati Bigali, said: "We are not happy with this verdict". The groups say they are independent.
The UN Security Council demanded a 30-day countrywide ceasefire a week ago, but this has failed to take effect.
The army has been accused of targeting civilians, but it says it is trying to liberate the area from those Damascus describes as terrorists.
Eastern Ghouta remains one of the few areas outside their control, along with the northwestern province of Idlib which is partly controlled by al-Qaeda-linked militants.
Four civil defense officials were injured in the attacks.
Eastern Ghouta is one of the last major rebel-held areas of the country, which has been ravaged by civil war for nearly seven years.
"Instead of a much needed reprieve, we continue to see more fighting, more death, and more disturbing reports of hunger and hospitals being bombed".
The latest fighting came as the French president, Emmanuel Macron, and the United Nations secretary general, António Guterres, expressed "grave concern" about the humanitarian situation in the area in a telephone conversation late on Saturday. "This collective punishment of civilians is simply unacceptable", he added.