UNITED NATIONS -- One day after Ukraine鈥檚 president laid out a forceful case against Russia's invasion at the United Nations, the United States made its own assertions in front of the UN Security Council on Thursday about why Russia should face further censure and isolation. Minutes later, Russia came right back, calling the claims unfair and saying Ukraine is to blame.

Antony Blinken, the United States' top diplomat, spoke to Security Council members on Thursday, detailing allegations of what he called war crimes and other atrocities committed by Russia and urging them to 鈥渟end a clear message鈥 to the country to stop its nuclear threats.

Russia's foreign minister, Sergey Lavrov, addressed the Security Council shortly afterward, repeating his country鈥檚 frequent claims that Kyiv has long oppressed Russian speakers in Ukraine鈥檚 east 鈥 one of the explanations Moscow has offered for the invasion.

Ukraine鈥檚 Western allies 鈥渉ave been covering up the crimes of the Kyiv regime,鈥 said Lavrov, who was not in the room when Blinken and some other U.S. allies spoke. He appeared just before his own speech and departed immediately afterward.

The almost-exchange between the two top diplomats came on the heels of Ukrainian President Volodymyr Zelenskyy's demands for world leaders to punish Russia in a video speech delivered Wednesday, just hours after Moscow made an extraordinary announcement that it would mobilize some reservists for the war effort.

Buoyed by a counteroffensive that has retaken swaths of territory that the Russians seized, Zelenskyy vowed that his forces would not stop until they had reclaimed all of Ukraine.

鈥淲e can return the Ukrainian flag to our entire territory. We can do it with the force of arms,鈥 the president said in a speech delivered in English. 鈥淏ut we need time.鈥

Video speeches by Zelenskyy in an olive green T-shirt have become almost commonplace. But this speech was one of the most keenly anticipated at the UN General Assembly, where the war has dominated over conflicts in other regions.

On Thursday, Israel鈥檚 prime minister, Yair Lapid, delivered a speech focused on the Palestinians and included a call for the establishment of a Palestinian state.

鈥淎n agreement with the Palestinians, based on two states for two peoples, is the right thing for Israel鈥檚 security, for Israel鈥檚 economy and for the future of our children,鈥 Lapid said.

The speech, coming ahead of Nov. 1 elections, appeared to be part of an effort by Lapid to portray himself 鈥 both to voters and global leaders 鈥 as a statesman and moderate alternative to his main rival, hardline former Prime Minister Benjamin Netanyahu.

But it was short on details, and there is virtually no chance Lapid, who has long supported a two-state solution, will get to push forward with his vision. Israel鈥檚 parliament is dominated by parties that oppose Palestinian independence, and opinion polls forecast a similar result after the upcoming elections.

The Palestinians seek the West Bank, east Jerusalem and the Gaza Strip 鈥 territories captured by Israel in 1967 鈥 for an independent state, a position that enjoys wide international support.

While Lapid and dozens of other world leaders sought airtime for issues plaguing their own nations 鈥 including climate change, rising food costs, human rights and vaccine inequity 鈥 Ukraine remained at the centre of the UN General Assembly, popping up in speeches by leaders from all over the world decrying Russia's invasion of a sovereign country.

鈥淚t鈥檚 an attack on this very institution where we find ourselves today,鈥 said Moldovan President President Maia Sandu, whose country borders Ukraine.

U.S. President Joe Biden鈥檚 address, too, focused heavily on the war in Ukraine.

鈥淭his war is about extinguishing Ukraine鈥檚 right to exist as a state, plain and simple, and Ukraine鈥檚 right to exist as a people. Whoever you are, wherever you live, whatever you believe, that should make your blood run cold,鈥 he said. 鈥淚f nations can pursue their imperial ambitions without consequences, then we put at risk everything this very institution stands for. Everything.鈥

Russian President Vladimir Putin, who is not attending the General Assembly, has said he sent his armed forces into Ukraine because of risks to his country鈥檚 security from what he considers a hostile government in Kyiv; to liberate Russians living in Ukraine 鈥 especially its eastern region of the Donbas 鈥 from what he views as the Ukrainian government鈥檚 oppression; and to restore what he considers to be Russia鈥檚 historical territorial claims on the country.

Earlier this week, he warned that his nuclear-armed country will 鈥渃ertainly use all means available to us鈥 if its territory is threatened and to defend the country and its people.

Putin鈥檚 decree Wednesday about the mobilization was sparse on details but officials said as many as 300,000 reservists could be tapped. It was apparently an effort to seize momentum after the Ukrainian counteroffensive.

But the first such call-up in Russia since World War II also brought the fighting home in a new way for Russians and risked fanning domestic anxiety and antipathy toward the war. Shortly after Putin鈥檚 announcement, flights out of the country rapidly filled up, and more than 1,000 people were arrested at rare antiwar demonstrations across the country.

Zelenskky asserted that Moscow wants to spend the winter preparing its forces in Ukraine for a new offensive, or at least preparing fortifications while mobilizing more troops in the largest military conflict in Europe since World War II

鈥淩ussia wants war. It鈥檚 true. But Russia will not be able to stop the course of history,鈥 he said, declaring that 鈥渕ankind and the international law are stronger鈥 than what he called a 鈥渢errorist state.鈥

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Associated Press journalists Andrew Katell in New York and Josef Federman in Jerusalem contributed to this report.