The Syrian government says its belief in victory is "even greater" because the Syrian army is progressing in the war against terrorism, while the Syrian opposition plans to meet to decide whether to continue with stalled UN-led peace talks.
Syrian Foreign Minister Walid al-Moualem was speaking at the annual UN gathering of world leaders, after the Syrian army and allied militia seized ground north of Aleppo on Saturday, tightening a siege of the city's rebel-held east.
"Our belief in victory is even greater now that the Syrian Arab Army is making great strides in its war against terrorism, with the support of the true friends of the Syrian people, notably the Russian Federation, Iran and the Lebanese national resistance," Moualem told the 193-member General Assembly.
UN Secretary-General Ban Ki-moon is "appalled by the chilling military escalation" in Aleppo, his spokesman said.
"Since the announcement two days ago by the Syrian Army of an offensive to capture eastern Aleppo, there have been repeated reports of air strikes involving the use of incendiary weapons and advanced munitions such as bunker buster bombs," UN spokesman Stephane Dujarric said in a statement on Saturday.
"The secretary-general considers this a dark day for the global commitment to protect civilians," he said.
US Secretary of State John Kerry and Russian Foreign Minister Sergei Lavrov met several times this week in New York to try to revive a deal the pair agreed on September 9 aimed at putting Syria's peace process back on track.
The deal included a nationwide truce to improve humanitarian aid access and the possibility of joint military operations against Islamic State militants and al-Qaida-linked Nusra Front.
The truce effectively collapsed after a week when an aid convoy was bombed on Monday, killing about 20 people. Then on Thursday the Syrian army announced a major new offensive to win full control of Aleppo.
"I call on the United States of America, from here in New York, to take urgent measures - military, political and diplomatic measures - to protect the Syrian people," Syria's chief opposition co-ordinator Riad Hijab told reporters.
Hijab said he has called a meeting of Syria's mainstream political opposition, the Riyadh-based High Negotiations Committee, in the coming days to consider "the future of the political process, which is clearly being used by the regime's allies to achieve gains on the ground."
The issues at the heart of the current talks is a US demand for Russia and Syria to ground their warplanes for seven days to allow aid to get to besieged communities and for opposition groups to separate from Nusra Front, diplomats said.
Hijab said on Saturday that there was "no longer any use" for partial truces.
"I know there is no Plan B and that is why we are demanding the US to do something and let there be a Plan B," he said.
"What is happening in Aleppo today is unacceptable. It's beyond the pale," Kerry said in Boston on Saturday before meeting with his counterparts from the European Union, Britain, France, Germany and Italy.
"If people are serious about wanting a peaceful outcome to this war then they should cease and desist bombing innocent women and children, cease cutting off water and laying siege in medieval terms to an entire community," he said.