US Ambassador to the United Nations Linda Thomas-Greenfield said the vote will see where other nations stand on the issue on the anniversary of the war.
The European Union's top diplomat, Jose Borrell, noted that not stopping Russia will increase the "risk for any other country elsewhere in the world to face a similar aggression."
Russia's UN Representative told the General Assembly on Wednesday that the West was "ready to plunge the entire world into the abyss of war" over its support of Ukraine.
During the high-level meeting, Russia's Permanent Representative to the United Nations, Vasily Nebenzya, defended Russia's position.
Nebenzia told the General Assembly the West has ignored Russia's concerns and continued "bringing the military infrastructure of Nato closer and closer" to its borders.
Nebenzia said Moscow "had no other option" but to launch what it has called a "special military operation" on Feb. 24 last year to defend Russian speakers in eastern Ukraine and ensure "the safety and security of our country, using military means."
The General Assembly appeared set to adopt a resolution on Thursday, put forward by Ukraine and supporters, stressing "the need to reach, as soon as possible, a comprehensive, just and lasting peace" in line with the founding UN Charter.
Ukraine and its supporters hope to deepen Russia's diplomatic isolation by seeking yes votes from nearly three-quarters of the General Assembly to match - if not better - the support received for several resolutions last year.
They argue the war is a simple case of one unprovoked country illegally invading another, while Russia portrays itself as battling a "proxy war" with the West, which has been arming Ukraine and imposing sanctions on Moscow since the invasion.
The draft UN resolution, which is non-binding, but carries political weight, mirrors a demand the General Assembly made last year for Moscow to withdraw troops and halt the hostilities. Russia has described the text as "unbalanced and anti-Russian" and urged countries to vote no.
UN chief denounces Russia
United Nations Secretary-General Antonio Guterres on Wednesday denounced Russia's invasion of Ukraine as a violation of the founding UN Charter and international law and called out Russian threats about the possible use of nuclear weapons.
Since Moscow invaded its neighbour on Feb. 24 last year, Russian President Vladimir Putin has repeatedly hinted that Russia could use a nuclear weapon if threatened.
"We have heard implicit threats to use nuclear weapons. The so-called tactical use of nuclear weapons is utterly unacceptable. It is high time to step back from the brink," Guterres told the 193-member UN General Assembly at a meeting to mark the first anniversary of the war in Ukraine.
Guterres described the UN Charter as "unambiguous," citing: "All members shall refrain in their international relations from the threat or use of force against the territorial integrity or political independence of any state."
"The position of the United Nations is unequivocal: We are committed to the sovereignty, independence, unity and territorial integrity of Ukraine, within its internationally recognized borders," Guterres said.
Ukrainian Foreign Minister Dmytro Kuleba told reporters that Ukraine was exercising its right to self-defence as enshrined in the UN Charter and that "when you are sending weapons to Ukraine, you are helping Ukraine to defend UN Charter."
"Russia has said it launched a "special military operation" to "denazify" Ukraine and protect Russian speakers, and has also accused the West of waging a "proxy war" against it by arming Ukraine and imposing sanctions on Moscow.
The United States and its western allies have called the invasion an unprovoked land grab against a sovereign nation.
Reuters