"The longer the fighting drags on, the more civilians will be caught in the middle, the more they will pay the highest price," Samantha Power told the Security Council which met to discuss the crisis in Aleppo.
Syrian rebel forces on Sunday announced a bid to capture all of the city after joining up with jihadists on the weekend to open a route into besieged eastern Aleppo.
Fighting for the city entered a new phase last month when government forces took control of the last supply road into rebel-held areas, leaving some 250,000 people in eastern districts surrounded.
"The fighting of the past few days confirms what we have known for a very long time," said Power.
"Despite the overwhelming force of the Assad regime, Russian, Iran and Hezbollah on one side, neither side will be able to win a swift or decisive victory in the battle for Aleppo," she added.
Council members heard accounts from Syrian doctors who showed graphic pictures of children wounded in barrel bomb attacks and reported that they had been unable to save them because of a shortage of medicine.
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"What we have seen in Aleppo is beyond words," said Zaher Sahloul, a doctor from the Syrian American Medical Society.
Sahloul invited council members to visit Aleppo to meet with doctors and nurses fighting to save lives.
French Deputy Ambassador Alexis Lamek warned that the fighting in Aleppo could kill off any prospects for the peace process launched in Vienna to try to end the five-year war.
"Aleppo could become the grave of the Vienna process," said Lamek.
The United Nations is hoping to re-launch peace talks in late August, but that effort is conditional on progress in delivering humanitarian aid to civilians.
More than 290,000 people have been killed since Syria's conflict erupted in March 2011, the Observatory said in a new toll on Monday.
The deaths included more than 84,000 civilians.