The General Assembly will vote this week on a draft resolution similar to a text vetoed by Russia in the 15-member Security Council on Friday.
No country has a veto in the General Assembly and Western diplomats expect the resolution, which needs two-thirds support, to be adopted. While General Assembly resolutions are non-binding, they carry political weight.
Western states see action at the UN as a chance to show Russia is isolated because of its invasion of its southwestern neighbour.
The draft resolution already has at least 80 co-sponsors, diplomats said on Monday. More than 100 countries are due to speak before the General Assembly votes.
"No one can avert their gaze, abstention is not an option," French UN Ambassador Nicolas de Riviere said.
Ceasefire talks between Russian and Ukrainian officials failed to make a breakthrough on Monday.
UN Secretary-General Antonio Guterres said he hoped the talks would "produce not only an immediate halt to the fighting, but also a path towards a diplomatic solution".
He described Russian President Vladimir Putin's decision on Sunday to put Russia's nuclear deterrent on high alert as a "chilling development", telling the General Assembly nuclear conflict is "inconceivable".
Ukraine's UN Ambassador Sergiy Kyslytsya described Putin's order to put Russian nuclear forces on alert as "madness".
"If he wants to kill himself he doesn't have to use a nuclear arsenal, he has to do what the guy in Berlin did in a bunker in 1945," Kyslytsya told the General Assembly, referencing Adolf Hitler's suicide.
Guterres also warned about the impact of the conflict on civilians and said it could become Europe's worst humanitarian and refugee crisis in decades.
"Although Russian strikes are reportedly largely targeting Ukrainian military facilities, we have credible accounts of residential buildings, critical civilian infrastructure and other non-military targets sustaining heavy damage," he said.
Russia's UN Ambassador Vassily Nebenzia said Russia's actions in Ukraine were being "distorted".
"The Russian army does not pose a threat to the civilians of Ukraine, is not shelling civilian areas," he told the General Assembly.
Russia calls its actions in Ukraine a "special operation" it says is not designed to occupy territory but to destroy its southern neighbour's military capabilities and capture what it regards as dangerous nationalists.
UN aid chief Martin Griffiths briefed the Security Council later on Monday on the humanitarian situation in Ukraine.
"The scale of civilian casualties and damage to civilian infrastructure, even in these very early days, is alarming," Griffiths told the council.
"Civilian children, women and men have been injured and killed."
UN refugee chief Filippo Grandi said the agency is planning for up to four million refugees in the coming days and weeks.
