UN special envoy Staffan de Mistura said the offensive to retake rebel-held eastern Aleppo may amount to war crimes
Russia is partnering with the Syrian government to carry out war crimes, Britain's ambassador to the UN has said.
Speaking at an emergency meeting of the UN Security Council, Matthew Rycroft said the push by the US and Russia to stop the fighting is "nearing the end of its life".
But UN Secretary-General Ban Ki-moon urged world powers to redouble their efforts to end Syria's "nightmare".
He said: "What excuse is there for anything less than determined action to stop the mayhem?
"How much longer will all those with influence allow such cruelty to continue?
"I urge all involved to work harder for an end to the nightmare."
Washington and Moscow brokered a ceasefire after weeks of negotiations earlier this month, but the agreement collapsed on Monday.
The UN's top envoy to Syria accused the country's government of unleashing "unprecedented military violence" against civilians in the city in the aftermath of the collapse of the truce.
Staffan de Mistura said the offensive to retake rebel-held eastern Aleppo, which involved targeting civilians with sophisticated weapons including incendiary devices, may amount to war crimes.
The meeting comes as pro-government forces continue their intense bombardment of Aleppo, with the British-based Syrian Observatory for Human Rights saying at least 23 people were killed in the latest airstrikes on Sunday.
The deteriorating situation in the country represents a "moment of truth" for the UN, France's foreign minister Jean-Marc Ayrault warned, while US ambassador Samantha Power said Moscow's actions in Syria were "barbarism, not counter-terrorism".
Russia's UN ambassador Vitaly Churkin told the session that bringing peace to Syria "is almost an impossible task now".
Meanwhile, Mr Rycroft, Ms Power and French ambassador Francois Delattre walked out of the Security Council when Syria's ambassador was called to speak - in a show of anger and frustration by the West.
Syrian rebels had declared the push for peace "futile" after Syrian government and Russian warplanes bombarded Aleppo in the worst surge of violence in the city for years.
The 30 rebel groups - including the biggest faction backed by Turkey, Gulf states and the West - said the bombing campaign was "unprecedented", with more than 200 killed in recent days.
Efforts to revive such an agreement are now a lost cause unless there is an immediate end to fighting and aid is forthcoming, rebels said.
The statement also said rebels could not accept "Russia as a sponsor because it was a partner with the regime in its crimes against our people".
And it claimed Russian-backed Syrian forces were using napalm and chemical weapons without censure by the international community.
Warplanes have bombed a strategic camp on the northern edge of Aleppo, as Syrian government and rebel forces battle for control of the high ground.
Jets have also continued to hit residential parts of the town, rebels and residents said.
More than 250,000 civilians are trapped in the rebel-held areas in the east of Aleppo.
As well as strikes from the air, the Syrian army is also attempting to make gains on the ground.
Troops, along with militia allies, seized control of the Handarat Palestinian refugee camp, a few miles north of Aleppo, only for rebel forces to counterattack hours later.
"We retook the camp," said Abu al-Hassanien, a rebel commander. "But the regime burnt it with phosphorous bombs. We were able to protect it, but the bombing burnt our vehicles."
The Syrian army, which is supported by Iranian-backed militias, Lebanon's Shia Hezbollah militant group and a Palestinian militia, acknowledged rebels had retaken the largely uninhabited camp.
The area is near Castello Road, an important supply route to the city's rebel-held areas.
Residents say the airstrikes since the army offensive was announced on Thursday have been worse than ever, with more powerful bombs used.
The Syrian Observatory for Human Rights, a British-based monitoring group, said at least 45 people, including 10 children, were killed in eastern Aleppo on Saturday.
The Observatory said 213 civilians have been killed by airstrikes and shelling in and around Aleppo since the ceasefire expired on Monday.
The army says it is only targeting militants.