Thousands of Syrians are fleeing a government-led offensive on the rebel-held Eastern Ghouta enclave near Damascus as President Bashar al-Assad vowed the fight would continue until the "embrace of terrorism" was eradicated.

Syrian government forces have seized roughly one-quarter of the territory in recent days, the Syrian Observatory for Human Rights said on Sunday. Backed by Russian air power, the Syrian military has advanced on several fronts, retaking control of farms and villages, state media reported.

Government forces seized a number of districts including Al-Nashabiyeh and Otaya and had "eradicated terrorist groups" on the eastern outskirts of Damascus, state media quoted a military source as saying.

They have reached the centre of the besieged enclave to the edge of Beit Sawa, according to the UK-based Syrian Observatory. The Central Military Media said Syrian forces reached the outskirts of Mesraba, in central Ghouta.

Rebels were forced to retreat and regroup in Eastern Ghouta because of the Syrian government's "scorched earth" policy involving heavy artillery fire, air strikes, and helicopter attacks, a spokesman for the Jaish al-Islam rebel group said on Sunday.

In a voice message, spokesman Hamza Birqdar vowed government forces would be driven from the territory they had captured. The rebels had fortified positions to confront the attacking forces, he added.

Eastern Ghouta, home to some 400,000 people, has been under a crippling siege and daily bombardment for months. More than 600 civilians have been killed in the last two weeks alone.

'Destruction everywhere'

An AFP news agency correspondent inside Eastern Ghouta saw hundreds of civilians on Sunday fleeing from the town of Beit Sawa in the southeast of the enclave.

The Syrian Observatory said some 2,000 civilians had fled regime shelling and clashes in eastern areas to western parts of the enclave.

"Everyone is on the road. There's destruction everywhere," said 35-year-old Abu Khalil, carrying a little girl in his arms with a wound to her face. "Many families are trapped under rubble, the rescue workers just can't cope."

Assad's forces have seized more than one-quarter of the enclave on Damascus's eastern edges after two weeks of devastating bombardment.

"The majority [of people] in Eastern Ghouta want to escape the embrace of terrorism. The operation must continue," Assad said remarks broadcast on state television.

In a statement Sunday, the UN said it plans to deliver aid to Douma, the largest town in Eastern Ghouta, with its partners on the ground. An aid convoy consisting of 46 truckloads will be allowed in Monday with health and nutrition supplies and food for 27,500. The convoy will be led by Ali al-Za'atri, the UN resident humanitarian coordinator in Syria.

"We hope that the convoy may proceed as planned and will be followed by other convoys," Za'atri said.

The UN said it has received assurances the next convoy will be delivered on March 8.