The United Nations is expecting civilian evacuations out of rebel-held Eastern Ghouta on Tuesday, as the Syrian government military continues its fierce offensive on the enclave.

"This day, we are expecting evacuation of civilians, including people with medical conditions," Ali al-Zatari, the UN's top aid official in Syria, told Reuters news agency at al-Wafideen crossing, without elaborating.

The UN has previously called for the evacuation of nearly 1,000 sick and wounded residents who need urgent medical treatment.

Jaish al-Islam, one of the main rebel groups in Eastern Ghouta, said on Monday it had reached an agreement with the government's key ally, Russia, to evacuate wounded people. No other details about the evacuation were given.

Hamza Birqdar, the group's military spokesman, vowed on Tuesday that the fighters would defend the Damascus suburb till the end.

Syrian state TV showed a group of civilians leaving the enclave on Tuesday morning. The evacuations have not been independently confirmed.

The Syrian army's campaign of air and artillery attacks has killed more than 1,100 civilians in nearly a month, according to the UN Office for the Coordination of Humanitarian Affairs.

Syrian government forces have captured more than half the enclave, splintering it as they seek to crush the last major rebel bastion near the capital Damascus.

Their advances have cut off Douma and Harasta from each other and from other neighbouring towns.

Families are sleeping in the open in the streets in Douma, Ghouta's biggest town, with no more room in basements to shelter from the bombs, local authorities have said.

'Act if we must'

On Monday, the United States threatened to "act if we must" as a ceasefire resolution by the UN Security Council continues to be ignored.

US ambassador to the UN Nikki Hailey denounced the failure to implement a UN resolution calling for a ceasefire, and said her country was drafting a new one with "no room for evasion". Haley warned the US "remains prepared to act if we must".

"It is not the path we prefer, but it is a path we have demonstrated we will take, and we are prepared to take again," Haley told the 15-member Security Council. "When the international community consistently fails to act, there are times when states are compelled to take their own action."

UN Secretary-General Antonio Guterres also urged the Security Council members to "end the suffering" of residents in Eastern Ghouta.

"I am deeply disappointed by all those ... who allowed this to happen," Guterres said in his address at the UN headquarters in New York.

"There should be only one agenda for all of us: to end the suffering of the Syrian people and find a political solution to the conflict.

"Particularly in Eastern Ghouta, the air strikes, shelling, ground offensive intensified after the adoption of the resolution," he said, referencing UNSC resolution 2401, which passed on February 24.

Resolution 2401 called for an immediate ceasefire, the evacuation of civilians, and the delivery of aid supplies.

Guterres also expressed his disappointment at the prevention of desperately needed food and medical assistance from being delivered to some of the 400,000 residents trapped inside the enclave.