They have splintered it into three besieged zones, the smallest of which is the Harasta pocket.
Scores of civilians were killed in a single air attack on eastern Ghouta yesterday, doctors said, as the battle for the Syrian rebel stronghold reaches a tipping point.
"Field kitchens have been deployed and hot meals are being distributed to civilians at the checkpoints and in refugee camps", Zolotukhin said.
The weekslong violence in eastern Ghouta has left about 1,400 civilians dead and more than 5,000 wounded.
A number of patients requiring urgent medical attention have been evacuated from the northern pocket and some aid has entered there.
The thousands of civilians streaming out of the enclave into regime-held areas on Saturday mostly came from this southern sector, it said.
The dire humanitarian situation in Eastern Ghouta, a suburb of the Syrian capital, is likely to be on the agenda as Mohammad Javad Zarif of Iran, Sergei Lavrov of Russian Federation and Mevlut Cavusoglu of Turkey convened in the Kazakh capital Astana Friday. Almost 1,260 civilians have been killed there, a fifth of them children, since the Syrian regime's bombardment of the rebel enclave began on February 18.
Government forces seized Kafr Batna and Sabqa in the south of the enclave, the British-based Syrian Observatory for Human Rights said, as thousands of civilians fled into regime-held territory.
More than 20,000 people have left Eastern Ghouta via Hammouriyeh so far on Sunday, the Interfax news agency reported, citing the Center for Reconciliation in Syria, a body run by Russia's Defense Ministry.
Russia's military also said early on Saturday that more than 11,000 people have left the enclave in the past few hours as regime forces step up the offensive.