Staffan de Mistura
Staffan de MisturaReuters

The United Nations warned Sunday that time was "running out" for efforts to avoid a humanitarian catastrophe in Syria's war-battered Aleppo, as fresh fighting there killed at least eight schoolchildren.

International concern has mounted since Damascus began a ferocious assault last Tuesday in an attempt to recapture eastern Aleppo.

In Damascus, UN envoy Staffan de Mistura was rebuffed on a truce proposal that would allow the opposition to administer the city's rebel-held east.

"We are running out of time, we are running against time," De Mistura warned after meeting Foreign Minister Walid Muallem.

Aid agencies fear that "instead of a humanitarian or a political initiative" there would be "an acceleration of military activities" in eastern Aleppo and elsewhere, the envoy told journalists.

"By Christmas... due to military intensification, you will have the virtual collapse of what is left in eastern Aleppo; you may have 200,000 people moving towards Turkey -- that would be a humanitarian catastrophe," he added.

Meanwhile, U.S. President Barack Obama urged greater efforts to end the violence when he met Russian President Vladimir Putin on the sidelines of an Asia-Pacific economic summit in Peru.

Obama "noted the need for Secretary (John) Kerry and Foreign Minister (Sergei) Lavrov to continue pursuing initiatives, together with the broader international community, to diminish the violence and alleviate the suffering of the Syrian people", a White House official said.

Earlier on Sunday, a rebel rocket attack killed at least eight primary school children in the Furqan neighborhood of the government-held west, state media said.

Syrian television showed bloodied, weeping children being treated in hospital, and an AFP journalist saw pupils being rushed from the school after the attack.

Closing the net further, regime forces broke through into the city's northeastern area of Massaken Hanano, sparking fierce clashes, the Syrian Observatory for Human Rights said.

The Britain-based monitoring group said at least 19 civilians including five children were killed in the east on Sunday.

That brought to 115 the number of civilians killed, including 18 children, since the bombardment of east Aleppo resumed, it said. At least 74 rebels have been killed.

On Thursday, Syrian air strikes and shelling killed 25 civilians in eastern districts of Aleppo.

On Wednesday, at least 21 people were killed, five of them children, when Syrian airstrikes damaged a children's hospital, a blood bank, and a school.

More than 300,000 people have been killed in Syria since the conflict began with anti-government protests in March 2011. Successive international attempts to find a peaceful resolution have failed.

De Mistura said he opened his talks with Muallem by "expressing serious concern and indeed shared the general international outrage for the news coming from eastern Aleppo".

Muallem said he had rejected a proposal for a deal that would recognize an autonomous rebel administration in east Aleppo.

De Mistura has recently floated a proposal to halt fighting in the city, under which jihadist forces would leave and the government would recognize the opposition administration in the east.

But Muallem said "we reject that completely".

"How is it possible that the UN wants to reward terrorists?" he asked. “Terrorists” is the term used by the Syrian regime to describe all the rebels – jihadist and moderate – trying to oust President Bashar Al-Assad.

The regime offensive has forced hospitals and schools to close and destroyed rescue worker facilities.

U.S. National Security Advisor Susan Rice said Washington condemned "in the strongest terms these horrific attacks against medical infrastructure and humanitarian aid workers".

AFP contributed to this report.