US Secretary of State John Kerry and Russia's Foreign Minister Sergei Lavrov gathered two dozen international envoys at talks in New York to address the crisis.
But the meeting of the International Syria Support Group broke up after Russia refused US demands that it promise to immediately ground the Syrian regime's air force.
Kerry said he was ready to meet the Russians again to see if there are any means to revive the truce that failed this week, but diplomats were pessimistic.
"Not for one day or two, but for as long as possible so that everyone sees that they are serious."
UN peace envoy Staffan de Mistura called it a "long, painful and disappointing meeting" but insisted that Washington and Moscow are serious about the truce.
He blamed unnamed other parties among the delegates for "undermining" the US-Russian initiative and added "they are still trying, so declaring it dead would be wrong."
"Meanwhile, what is happening in Aleppo is under attack and everyone is going back to the conflict," he said.
"The next few hours -- days at maximum -- are crucial for making it or breaking it."
In Damascus, the Syrian army urged residents of Aleppo to stay away "from the positions of terrorists" as it launched its new offensive in defiance of the truce.
London-based watchdog the Syrian Observatory for Human Rights described the latest assault as "a large-scale land offensive supported by Russian air strikes."
An AFP correspondent in the rebel-held east of Aleppo witnessed a dozen families fleeing the Soukkari district for other rebel areas further north.
The estimated 250,000 residents of east Aleppo, which rebels against Bashar al-Assad's have held since 2012, have been living under siege since early September.
The conflict in Syria has cost more than 300,000 lives since 2011, during which time more than half the population was uprooted from their homes.
On September 9, Kerry and Lavrov met in Geneva and agreed to call a ceasefire, with Moscow responsible for forcing Assad's forces to stand down and allow in UN aid convoys.
Diplomats believe the US-Russian Geneva process is the only available hope to end the five-year conflict, but Moscow and Washington have fallen out spectacularly.
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