Rouhani spoke in a televised address after Trump gave a much anticipated White House speech in which he "decertified" his support for the 2015 nuclear agreement, and left its fate in the hands of Congress.
"Today the United States is more than ever isolated in its opposition to the nuclear deal and in its plots against the Iranian people," Rouhani said.
"What was heard today was nothing but the repetition of baseless accusations and swear words that they have repeated for years," Rouhani said.
Rouhani dismissed Trump's threat to tear up the landmark deal between Tehran and six world powers including Washington if Congress does not impose tough new sanctions on Iran.
"He has not studied international law. Can a president annul a multilateral international treaty on his own?" Rouhani said.
"Apparently he doesn't know that this agreement is not a bilateral agreement solely between Iran and the United States."
Rouhani responded in kind to Trump's list of alleged destabilising activities in the region, with his own catalogue of US misdemeanours, starting with the CIA's involvement in a 1953 coup, which toppled Iran's democratically elected government.
Trump called for tougher sanctions on Iran's Revolutionary Guards and ballistic missile programme, and said the deal could still be "terminated" if Congress did not adequately confront "destabilising" Iranian activity in the Middle East.
But he stepped back from the sort of measures that would immediately torpedo the nuclear agreement.
Rouhani attacked Trump's characterisation of the Revolutionary Guards as a corrupt organisation propping up a "fanatical regime".
Despite Trump's aggressive rhetoric, Rouhani said Iran remained committed to the nuclear agreement for the time being.
"We respect the JCPOA... so long as it remains in keeping with our national rights and interests," he said, using its technical name.
Rouhani also responded to Trump's criticism regarding the frequently heard slogans of "Death to America" and "Death to Israel", which Iranians usually depict as opposition to the policies of those nations, rather than a call for their physical destruction.
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