"So long as the aggressor is a party to decision-making in the international organisations, he must be isolated from them," Zelensky said.
Russia hasn't yet had its turn to speak at the gathering. Putin has said he sent his armed forces into Ukraine because of risks to his country's security from what he considers a hostile government in Kyiv; to liberate Russians living in Ukraine — especially its eastern Donbas region — from what he views as the Ukrainian government's oppression; and to restore what he considers to be Russia's historical territorial claims on the country.
The war has dominated the global gathering, which comes nearly seven months after Russia launched what has become the largest military conflict in Europe since World War Two.
In a reflection of the circumstances, Zelensky wasn't at the rostrum where other presidents, prime ministers and monarchs speak at international diplomacy's most prominent annual gathering. Instead, he got an exception to speak via video.
As a permanent member of its most powerful entity, the Security Council, Russia was able to veto a demand to stop its attack on Ukraine days after it began.
But the move galled a number of other countries and led to action this spring in the broader General Assembly, where resolutions aren't binding but there are no vetoes.
The assembly voted overwhelmingly in March to deplore Russia's aggression against Ukraine, call for an immediate ceasefire and withdrawal of all Russian forces, and urge protection for millions of civilians. The next month, a smaller but still commanding number of members voted to suspend Russia from the UN Human Rights Council.
Putin's decree about the partial mobilisation was sparse on details. Officials said as many as 300,000 reservists could be tapped.
It's an apparent effort to seize momentum after a Ukrainian counteroffensive this month retook swaths of territory that Russians had held.
But the first such call-up in Russia since World War Two also brings the fighting home in a new way for Russians and risks fanning domestic anxiety and antipathy toward the war.
Shortly after Putin's announcement, flights out of the country rapidly filled up as people scrambled to book one-way tickets and prices spiked. Hundreds of people were arrested at antiwar demonstrations across the country.
A day earlier, Russian-controlled parts of eastern and southern Ukraine announced plans for referenda on becoming parts of Russia. Ukrainian leaders and their Western allies consider the votes illegitimate.
Zelensky's speech was one of the most keenly anticipated at a gathering that has dwelled this year on the war in his country. But it wasn't the first time the first-term president has found himself in the spotlight at the assembly's annual meeting of presidents, premiers, monarchs and foreign ministers.
At last year's General Assembly meeting, Zelensky memorably compared the UN to "a retired superhero who's long forgotten how great they once were" as he repeated appeals for action to confront Russia over its 2014 annexation of the Crimean peninsula and its support for the separatists.