Syria’s military appears to be increasing pressure on several fronts to try to retake the enclave just to the east of the capital, Damascus.
Government forces have taken 10% of the area, the Syrian Observatory for Human Rights says.
A UN aid convoy planned for Sunday has not been able to enter the enclave.
The UN said it had failed to obtain permission from Syrian officials for 40 trucks carrying humanitarian supplies for the key town of Douma.
In a statement, the UN said the “collective punishment of civilians is simply unacceptable”.
Some 393,000 people are trapped in the besieged enclave.
Neither a daily five-hour truce ordered by the Russians – Syria’s main backers – nor a nationwide ceasefire demanded by the UN Security Council have led to any humanitarian relief for the enclave.
Opposition sources and journalists on the ground speak of hundreds of people fleeing the bombardment of Beit Sawa on the eastern edge of the densely populated centre of the Eastern Ghouta – a sizeable region which also comprises towns and agricultural land.
A resident speaking to the BBC described the situation in the Eastern Ghouta as “beyond critical”.
Residents are reported to have fled into the centre of the enclave to seek shelter.
Several reports suggest government forces are attempting to cut the region in two.
Syria’s military says it is trying to liberate the region, one of the last rebel strongholds, from those it terms terrorists. But it has also been accused of targeting civilians.
The fighting since 18 February has left 650 people dead, more than 150 of them children. (Courtesy BBC)