HAMMURIYEH/ ISTANBUL - New air strikes and barrel bombs pounded Syria's Eastern Ghouta on Sunday as government forces pressed a three-week advance that splintered the rebel enclave and trapped dozens under collapsed buildings.

Defying global calls for a ceasefire, Syria's government has pursued a ferocious Russian-backed air campaign and ground offensive to capture the region, the last rebel bastion on the capital's doorstep.

In three weeks of fighting, it has overrun more than half the area and split the remainder into three pockets, isolating the urban hub of Douma from the rest of the enclave.

On Sunday, government troops battered the edges of each pocket with air raids, barrel bombs, and rockets, said the Britain-based Syrian Observatory for Human Rights. After fighting all morning, they captured the town of Medeira, which lies at the heart of the three zones, Observatory head Rami Abdel Rahman said.

State news agency SANA had reported troops were focusing on the town in order to cut rebel access routes in Ghouta.

Bombing runs across several towns in Ghouta killed a dozen civilians on Sunday, bringing the total toll from the offensive to at least 1,111 civilians, the Observatory said. They include dozens of decomposing bodies still trapped under pulverised residential blocks in the towns of Hammuriyeh, Saqba, and Misraba.

In Hammuriyeh, AFP's correspondent saw a young man scrambling frantically over the rubble of a collapsed building in search of his loved ones.

His father, mother, and three siblings were killed in an air raid, but rescue workers have been unable to pull them out.

Hassaan, a 30-year-old rescue worker, said there were around 20 more families under the rubble.

"We need heavy machinery to get them out, but we can't bring the machines out into the streets because the regime may bomb them," he said.

In the main town of Douma, bodies piled up in the morgue as bombardment prevented families from reaching the cemetery, AFP's correspondent there said. Families grew desperate for news of loved ones who had fled to other areas that were now inaccessible. SANA reported on Sunday that troops transported "dozens of civilians, including women and children," from Misraba to temporary shelters in government-held zones. The Observatory told AFP that Misraba was left abandoned after 75 to 100 people were moved out of the town by regime forces.

On Sunday, four people were killed and six wounded in rebel rocket fire on a government-controlled district in eastern Damascus, state television reported.

It broadcast live footage from the battered skyline of Medeira, saying Sunday's gains linked Syrian soldiers advancing from the east with troops based on the western edges of Ghouta.

On Sunday, US Defence Secretary Jim Mattis warned it would be "very unwise" for Assad to use weaponised gas against civilians, but delined to say whether doing so would trigger a US military response.

Meanwhile, Turkish President Recep Tayyip Erdogan on Sunday angrily lashed out at NATO, accusing the Western military alliance of failing to back Turkey's campaign against Kurdish militia in Syria.

Erdogan's latest comments were among the toughest he has directed in recent times against NATO, which Turkey joined in 1952 as the US sought to make sure it did not fall under Soviet sway after World War II.

Turkey launched its operation on January 20 seeking to oust the Kurdish People's Protection Units (YPG) from the Afrin region of northern Syria with its forces now just a few kilometres away from Afrin town.

But the YPG has been a key American ally in the fight against jihadists in Syria and the operation has raised tensions with Washington and European NATO powers, notably France. "Hey NATO! With what has been going on in Syria, when are you going to come and be alongside us?" Erdogan said in remarks to supporters in Bolu, a city east of Istanbul.

"We are constantly harassed by terror groups on our borders," he said. "Unfortunately until now, there has not been a positive word or voice."

After the start of the campaign, NATO Secretary General Jens Stoltenberg said Turkey had a right to defend itself but emphasised it must be done "in a proportionate and measured way."

Erdogan slammed Washington for arming the YPG, saying the group had received 5,000 trucks and 2,000 cargo planes of weapons.

"Is this friendship? Is this NATO unity?" he asked in a later speech, noting how Turkey had backed the alliance by participating in its operations in Afghanistan and elsewhere. "Are we not a NATO member?"

He also said Turkish troops and allied Syrian rebels were now just four to five kilometres (about three miles) from Afrin which they were poised to take.