Zelensky made the comment in passing at a conference in Kyiv as he was asked a question about the Russian president.
The general staff of Ukraine's armed forces described a "partial success" near the eastern city of Bakhmut, long a focal point of fighting.
Ukraine has long complained about lukewarm Israeli support as it defends itself against Russia’s invasion of its country, a war that is now in its second year.
Putin had initially made these claims about the Ukrainian president in a television interview on Tuesday.
The US government has so far provided more than $43 billion in weaponry and other military aid to Ukraine.
In justifying its invasion of Ukraine, Russia accuses Kyiv's leaders of being neo-Nazis pursuing a "genocide" of Russian-speakers.
The decision comes amid a crackdown on corruption in Ukraine that Zelensky has been keen to emphasize.
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