Secretary General Ban Ki-moon has said the world is facing a 'make or break moment'
US Secretary of State John Kerry has called for aircraft to be grounded in parts of Syria so a ceasefire deal can be extended.
Mr Kerry said he believed there was a way forward "out of the carnage", but that the future of the country was "hanging by a thread".
He added that international diplomats were proving "woefully inadequate" in getting Syrian parties to negotiate.
His impassioned speech at the United Nations followed an attack on an aid convoy on Monday and came as fighting broke out on numerous fronts in the war-torn country.
The airstrike, which killed some 20 aid workers delivering humanitarian supplies to civilians, "raises profound doubt" as to whether Russia and the Syrian government will live up to a ceasefire deal, Mr Kerry said.
Syrian government forces should be banned from flying over areas controlled by the opposition in an effort to help bring the escalating situation under control, he added, before urging countries to cease support to any parties attempting to sabotage a truce.
Secretary General Ban Ki-moon had previously told UN Security Council the world was facing a "make or break moment" in Syria, as there were multiple reports of fighting between Syrian rebels and pro-government forces:
Russia's foreign minister Sergei Lavrov said he wanted to see a thorough and impartial investigation into the attack on the aid convoy, after the Moscow released footage it said showed a pickup truck carrying a mortar travelling with the trucks.
No one has yet claimed responsibility for the airstrike on the aid convoy. The US believes two Russian Su-24 jets carried out the attack, based on location and timing.
But Moscow has denied all involvement, instead suggesting a fire broke out destroying the vehicles among other theories.
A Russian military spokesman said today that a Predator drone from the US-led coalition had entered the area where the attack had taken place "several minutes before it burst into flames".
Igor Konashenkov, a spokesman for the ministry, said allegations that Moscow was responsible were an attempt to distract attention from the US-led coalition's bombing of Syrian soldiers near Deir al-Zor airport on Saturday.
British Foreign Secretary Boris Johnson also spoke at the meeting, saying there could be no political process unless there was a genuine ceasefire.
The truce came into effect on 12 September in order to create a safe corridor for aid into war-torn Aleppo, where many of the inhabitants are said to be in dire need.
All aid convoys in Syria are currently suspended.