Syria’s military claimed about 25 percent of the Damascus suburb, monitors for the U.K.-based Syrian Observatory for Human Rights said.
A United Nations aid convoy planned for Sunday hasn’t been able to enter the enclave amid the fighting.
Government forces advanced from several fronts, mostly gaining control of villages and farms controlled by the al-Nusra Front on the eastern side of the enclave, according to state media.
The rebel group Jaish al-Islam issued a statement saying it retreated from two areas in Eastern Ghouta and accused the Syrian regime of employing a “scorched earth” strategy of bombardment.
Hundreds of people reportedly fled the bombardment and headed westward, where fighting is less intense.