By Jomana Karadsheh, Tamara Qiblawi and Lauren Said-Moorhouse, CNN

(CNN) -- The Syrian regime and its allies have splintered the rebel-held enclave of Eastern Ghouta into three parts after the army intensified its onslaught in the region over the weekend, an activist on the ground and state media said.

Syrian regime forces advanced Sunday to cut off Douma, the largest city in Eastern Ghouta and the main rebel supply route, media activist Bilal Abu Salah told CNN.

The town of Harasta was also isolated from the rest of the enclave by regime forces, which additionally broke off several central and southern towns and villages in Eastern Ghouta, he added.

Syrian state media reported on Sunday that "army units have completely cut off supply routes and movement lines of terrorist organizations between the northern and southern parts of Ghouta, which should accelerate the defeat of terrorists in the area."

Since launching its offensive against the enclave in mid-February, the Syrian regime has steadily been gaining territory, starting with villages and towns in the east.

Analysts believe it is now a matter of time before the regime takes control of the entire enclave, one of the last major rebel-held areas in the country, which is situated on the outskirts of Damascus.

Related: Syrian regime continues to gain ground

Over 1,000 people were killed -- an average of 71 per day -- and 4,800 wounded in the first two weeks of the offensive, humanitarian group Doctors Without Borders, or Médecins Sans Frontières (MSF), said last week.

The numbers, which do not take into account people not treated at MSF medical facilities, are believed to be a fraction of the total death toll.

The regime maintains that its offensive is against fighters affiliated with Jabhat al-Nusra -- a former Qaeda affiliate that has rebranded itself several times and goes by several names -- whom it accuses of holding civilians against their will to use as human shields.

Armed rebel groups in the besieged enclave deny both accusations, saying al-Nusra's presence is limited and that civilians fear regime retaliation if they leave.

'Mass graves' and overcrowded basements

Jaish al-Islam, one of the armed rebel groups in the area, claimed on Monday that an agreement to evacuate the wounded from Eastern Ghouta had been reached. In a statement the group said the deal was reached with Russia -- a key ally of the Syrian regime -- through the mediation of the United Nations.

It was unclear which parts of Eastern Ghouta the deal would cover.

But Abo Ammar Alwan, head of the political bureau of Jaish al-Islam in Eastern Ghouta, told CNN that so far on Monday, no evacuations had taken place yet.

Earlier on Monday, activists in the region told CNN that the humanitarian situation has gone from bad to worse. The ground offensive has triggered a "massive" influx of displaced people into the cities, may of whom have sought refuge underground.

"Yesterday, after three days of being unable to bury our dead, we've had to put them in mass graves. The situation is very bad," said Bayan Rehan, head of the women's office at Douma's Local Coordination Committee.

Some residents have resorted to burying the dead in public parks, Firas Abdullah, a White Helmets spokesperson in Eastern Ghouta, told CNN.

"People are burying the dead in public parks inside the city due to the regime imminently completely encircling the city of Douma, and its cutting off from the rest of Eastern Ghouta," Abdullah said. "So the cemeteries are very close to the front lines and they are also full. So people have resorted to burying their dead in public parks."

Another activist in Eastern Ghouta told CNN that relief supplies have all but stopped because the main warehouse housing the supplies had been taken over by the regime and destroyed. Additionally, farmland that once provided food to residents had also been taken over by the regime.

Thirteen aid trucks carrying much-needed food parcels and wheat flour finally reached Douma on Friday. The trucks were delivering materials that aid workers said couldn't be offloaded from a first convoy earlier in the week, according to the International Committee of the Red Cross Syria.

But the aid was just a tiny portion of what Eastern Ghouta needed, activists said. The convoys were intended for 70,000 people in Douma, far less than the broader suburb's besieged population of 393,000.

One activist told CNN that basements there were overcrowded as residents sought protection from the unrelenting airstrikes. One makeshift shelter has housed some 200 families. As food supplies have dwindled, many have taken to slaughtering their animals -- mostly cows -- to stave off hunger.

Videos have emerged on social media showing Eastern Ghouta residents demonstrating in support of the regime. The activist told CNN that people support an end to the fighting more than anything else.

"You might see civilians going out with regime flags, but it's not because they want the regime -- they just want an end to bloodshed," the activist said. "They don't want to see their children burning or dying in front of them."