Biden hosted the Ukrainian president at the White House on Tuesday, public broadcaster Polish Radio's IAR news agency reported.
The US president urged Congress to "stand with Ukraine" amid the Russian invasion and approve USD 61 billion in military assistance for Kyiv.
Biden said that Russia planned to "bombard Ukraine’s electric grid" in the winter and that the West must not let the Kremlin "succeed in that."
Speaking to reporters alongside Zelensky, the US president also announced USD 200 million in further military aid for Ukraine that officials said "will be coming quickly."
Meanwhile, Ukraine's president thanked the United States and other allies for supporting his country's war effort against the Russian invasion, the IAR news agency reported.
Zelensky stated that "Ukraine can win."
Earlier on Tuesday, Ukraine's president met with US lawmakers on Capitol Hill, including senators in a closed-door gathering, to persuade them to back the USD 61 billion security package for Kyiv, Polish state news agency PAP reported.
Republicans have pushed back against the plan, demanding that Biden pair the Ukraine aid with tougher border policies, according to news outlets.
Wednesday is day 658 of Russia's war on Ukraine.
Russia invaded Ukraine on February 24, 2022, launching the largest military campaign in Europe since World War II.
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Source: IAR, PAP, White House, NBC News