“Regime forces assaulted Hammuriyeh and were able to control parts of it”, in the south of the enclave, the Britain-based Syrian Observatory for Human Rights monitoring group said.
Russia-backed regime forces on February 18 launched an assault on Eastern Ghouta to retake the last opposition bastion outside Damascus.
The offensive has split the enclave into three sections, each controlled by different rebels.
The area around Hammuriyeh is controlled by the Faylaq al-Rahman faction.
It has come under intense bombardment in recent days, an AFP correspondent there said.
On Wednesday, the correspondent saw a man in the doorway of a building holding the bodies of his two dead children.
A doctor in the area said rescue teams could not get to victims because of the intensity of the bombardment.
“The wounded are on the roads. We can’t move them. The war planes are targeting anything that moves,” Ismail al-Khateeb said.
“We don’t know what happened to the families that fled under the bombardment.”
More than 1,220 civilians have been killed in Eastern Ghouta since February 18.