"Trump's ignorant hate speech belongs in medieval times -- not the 21st century UN -- unworthy of a reply," Zarif said on Twitter.
"Fake empathy for Iranians fools no one," he added.
In his maiden speech to the UN General Assembly, Trump branded Iran a "corrupt dictatorship" and "rogue state" and said the "longest-suffering victims of Iran's leaders are, in fact, its own people."
Trump said the nuclear deal that Zarif negotiated in close cooperation with former US secretary of state John Kerry was "an embarrassment to the United States."
Trump appeared to pave the way towards tearing up the nuclear deal signed in 2015 between six world powers and Iran.
"We cannot let a murderous regime continue these destabilizing activities while building dangerous missiles, and we cannot abide by an agreement if it provides cover for the eventual construction of a nuclear program," he said.
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