President Biden emphasized unity and global cooperation Tuesday as he addressed the United Nations General Assembly in New York. Mr. Biden reiterated that Ukraine's interests are the United Nations' interests, and said the global body must "continue to preserve peace, prevent conflict and alleviate human suffering." 

"The United States seeks a more secure, more prosperous, more equitable world for all people, because we know our future is bound to yours," the president said at UNGA. "Let me repeat that again: We know our future is bound to yours. And no nation can meet the challenges of today alone." 

The president touted efforts to connect India and Europe, normalize relations between Israel and its neighbors, and strengthen African nations' infrastructure, and insisted he wants to "seek to responsibly manage" competition with China, not decouple from China. 

"Now let me be clear: None of these partnerships are about containing any country," the president said. "They're about a positive vision for our shared future. When it comes to China, I want to be clear and consistent — we seek to responsibly manage competition between our countries so it does not tip into conflict."

Where there is commonality on pressing global issues, the president said the U.S. needs to work with China. 

"We see it everywhere," Mr. Biden said. "Record breaking heatwaves in the United States and China," Mr.Biden said. "Wildfires ravaging North America and Southern Europe. A fifth-year of drought in the Horn of Africa. Tragic, tragic flooding in Libya ... Together, these snapshots tell an urgent story of what awaits us if we fail to reduce our dependence on fossil fuels and begin to climate-proof the world." 

The president's address comes after five U.S. citizens detained by Iran touched down on U.S. soil. They were freed Monday in a complicated diplomatic deal that included the transfer of $6 billion in unfrozen Iranian oil assets and the release of five Iranians facing charges in the U.S. 

Ukrainian President Volodymyr Zelenskyy will speak at UNGA Tuesday in his first in-person address to the assembly since Russian President Vladimir Putin launched an unprovoked assault on his country. Zelenskyy and Mr. Biden are also scheduled to meet at the White House on Thursday. 

"We strongly support Ukraine in its efforts to bring about a diplomatic resolution that delivers just and lasting peace," Mr. Biden said Tuesday. "But Russia alone, Russia alone bears responsibility for this war. Russia alone has the power to end this war immediately. And it's Russia alone that stands in the way of peace because the Russians' price for peace is Ukraine's capitulation, Ukraine's territory and Ukraine's children."

"Russia believes that the world will grow weary and allow it to brutalize Ukraine without consequence. But I ask you this: If we abandon the core principles of the United States to appease an aggressor, can any member state in this body feeling confident that they are protected? If we allow Ukraine to be carved up, is the independence of any nation secure?"

Zelenskyy, too, has warned that world order is what's at stake in the war in Ukraine. 

"If Ukraine falls, what will happen in 10 years? Just think about it. If [the Russians] reach Poland, what's next? A Third World War?" Zelenskyy said a 60 Minutes interview that aired Sunday.

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• United Nations General Assembly
• Joe Biden
• United Nations
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Kathryn Watson

Kathryn Watson is a politics reporter for CBS News Digital based in Washington, D.C.