Staffan de Mistura met Foreign Minister Walid Muallem in Damascus for talks on the escalating violence, but 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 said afterwards.
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"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."
International concern has been mounting since Damascus began a ferocious assault last Tuesday, using air strikes, barrel bombs and artillery fire in a bid to recapture eastern Aleppo.
Today, rebels retaliated with a barrage of rockets into the city's government-held west, killing at least eight primary school children in the Furqan neighbourhood, state media said.
Syrian television showed bloodied, weeping children being treated in hospital, and an AFP journalist saw pupils being rushed from the school and comforted after the attack.
In the east, another AFP journalist said streets were deserted, with only ambulances and rescue workers moving around.
The Syrian Observatory for Human Rights, a Britain-based monitoring group, said on Sunday that 54 people had been killed in the previous 24 hours, mostly civilians.
That brought to 103 the number of civilians killed, including 17 children, since the bombardment of east Aleppo resumed, it said.
The Observatory also reported heavy fighting between regime forces and rebels as the army sought to gain ground in the eastern Bustan al-Basha and Sheikh Saeed neighbourhoods.
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.
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