"We are running out of time, we are running against time," Staffan de Mistura said after talks in Damascus with Foreign Minister Walid Muallem.
The UN envoy said concern was running high among aid agencies that "instead of a humanitarian or a political initiative" there would be "an acceleration of military activities" in eastern Aleppo and elsewhere in Syria.
De Mistura said he discussed the escalating violence in Aleppo where government forces last Tuesday began a bid to retake the eastern rebel-held side of the city using air strikes, barrel bombs and artillery.
Dozens of people have been killed in the onslaught, most of them civilians, a monitor has said, and many have been wounded, overwhelming rescue workers in a city where hospitals are also hit.
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On Sunday, rebels retaliated with a barrage of rockets into government-held western Aleppo, killing at least eight children at a school, state media said.
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".
"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 warned.
The envoy also confirmed that Syria's regime had rejected a truce proposal that would have allowed the opposition to administer the eastern part of the city.
More than 300,000 people have been killed in Syria since the conflict began with anti-government protests in March 2011, and successive international attempts to find a peaceful resolution have failed.