In a statement released Sunday, the UN's Office for the Coordination of Humanitarian Affairs said it hoped to deliver aid to parts of the area on Monday.
Under growing global pressure to end the bloodshed, regime backer Russian Federation last week announced daily five-hour "humanitarian pauses" in the enclave.
Captain Ahmed Taqtaq of the allied Syrian forces in Marsawa village said they seized control of three villages in the last 10 days, fighting some 50 Syrian Kurdish fighters.
Several reports suggest government forces are attempting to cut the region in two. The YPG has been an important ally for the United States in the fight against the Islamic State in Iraq and Syria.
The Observatory said at least 12 regime fighters had been killed in overnight clashes. "It is a scorched-earth policy", said Ghouta-based activist Nour Adam.
People were seeking shelter in areas closer to the center of the Eastern Ghouta, said the resident, who estimated thousands were on the move.
The sources from the Syrian Civil Defense, also known as the White Helmets, said 31 civilians were killed in Duma district in airstrikes and missile attacks.
Despite the Security Council ceasefire and Vladimir Putin calling for daily "humanitarian pauses" in the conflict, bombing has continued in the region, where nearly 400,000 civilians have lived under siege since 2013.
Meanwhile, no civilians have left Ghouta through a humanitarian corridor set up by Russian Federation and the Syrian government almost a week ago. Rebel officials have consistently denied stopping civilians from leaving. The official said preparations are underway to deliver food to civilians in the besieged area.
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Regime forces seized up to a quarter of the rebel-held enclave in fighting that sent hundreds of civilians fleeing, the Syrian Observatory for Human Rights said yesterday.
It compared the situation to the attacks by Russian Federation and the Syrian government on Aleppo in 2016, where thousands of civilians were killed.
The White House also called on pro-regime forces to "immediately cease targeting medical infrastructure and civilians" in Eastern Ghouta. U.S. President Donald Trump and German Chancellor Angela Merkel called on Thursday for its immediate implementation, Reuters added.
This comes as the Syrian forces have made notable progress in the fight against the rebels in Eastern Ghouta.
Just one small convoy with a month's worth of supplies for 7,200 people has been allowed to enter Ghouta so far this year, in mid-February.
The Observatory said some 2,000 civilians had fled government shelling and clashes in eastern parts of the enclave.
But trucks loaded with aid have so far been unable to enter the enclave, according to the UN. The convoy will be led by Ali al-Za'tari, the United Nations resident humanitarian co-ordinator in Syria.
He said the USA has sent troops to Syria on their own disregarding worldwide law and the UN Security Council.