At least 124 people, mostly civilians, have been killed in the bombardment of rebel-held eastern Aleppo since the army on Thursday announced an operation to take it, the Syrian Observatory for Human Rights said.
"War crimes are being committed here in Aleppo," French Ambassador Francois Delattre said, calling for action to ensure the atrocities do not go unpunished.
Britain's envoy spoke of "a new hell" unleashed on Syrians with bunker-busting bombs and more sophisticated weaponry used in air strikes pummelling residential areas.
"It is difficult to deny that Russia is partnering with the Syrian regime to carry out war crimes," said British Ambassador Matthew Rycroft.
Britain, France and the United States had called for the urgent talks after days of intense diplomatic efforts to salvage a US-Russian ceasefire deal ended in failure at the weekend.
UN Secretary-General Ban Ki-moon warned that the "chilling" escalation making use of advanced weaponry against civilians could amount to war crimes.
Ban called on world powers to "work harder for an end to the nightmare" in Syria that has left more than 300,000 people dead and driven millions from their homes.
To protest the attacks in Aleppo, the US, French and British ambassadors walked out of the Security Council chamber as the Syrian ambassador delivered his remarks.
- Almost impossible peace -
Russia's Ambassador Vitaly Churkin conceded that the surge in violence over the past days meant that "bringing a peace is almost an impossible task now."
Churkin again laid blame for the failed diplomacy with the United States, accusing Washington of being unable to convince armed opposition groups that it backs on the ground to distance themselves from the Al-Qaeda-linked Nusra Front and abide by the ceasefire.
A US-Russian ceasefire deal that would have charted a way forward towards peace talks was broken by the "sabotage by the moderate opposition", he asserted.
Churkin however said that reviving the ceasefire was still a goal that Moscow could pursue if it was part of a "collective" effort on all sides.
Despite the recriminations, UN envoy Staffan de Mistura said a "tiny window of opportunity ... still exists" for Russia and the United States to help Syria.
He appealed for renewed efforts to allow Syria to "step away from the brink of more years of bloody conflict which risks to become even worse."
Residents said cluster bombs rained down on Saturday night on eastern parts of the city, where an estimated 250,000 people are living under a government siege.
At least 19 children were among those killed in the assault, which has included missile strikes, barrel bomb attacks and artillery fire, the Syrian observatory said.
"All night long they were dropping cluster bombs. I couldn't sleep until four in the morning," said 62-year-old Ahmed Hajar, who was out looking for bread in the Al-Kalasseh neighborhood.
- We're civilians here -
In the nearby neighborhood of Bab al-Nayrab, 30-year-old Imad Habush was baking bread in a small wood-burning oven outside his house.
"None of the bakeries are open any more because of the bombing and the shortages of fuel and flour, so people have started making their own bread," he said.
"I don't know why the regime is bombing us in this barbaric way. We're civilians here. We're not carrying weapons, and we're besieged. We have no way to escape."
Air strikes were continuing on the eastern neighborhoods on Sunday, the Observatory said, with at least 25 civilians, including two children, killed since dawn.
Once Syria's economic powerhouse, Aleppo has been ravaged by war and roughly divided since mid-2012 between government control in the west and rebel control in the east.
The eastern portion of the city has been under near-continuous siege since mid-July, causing food and fuel shortages.
A truce deal hammered out by Russia and the United States this month was meant to allow aid to be trucked into the east of the city.
But the ceasefire fell apart before any assistance was brought in. And the army and its Russian ally have since pounded the eastern neighborhoods with a force that residents say is virtually unprecedented.
More than 300,000 people have been killed and over half the country displaced since the war began in March 2011 with anti-government protests.
Successive attempts to reach a political solution have failed, and the latest bid by Moscow and Washington has virtually collapsed, despite ongoing talks to save it.
Syria's foreign minister said Saturday that his government was confident of "victory" with support from "true friends" including Russia, Iran, and Lebanon's Shiite militant group Hezbollah.
"Our belief in victory is even greater now that the Syrian Arab army is making great strides in its war against terrorism," Walid Muallem told the UN General Assembly.