Rouhani spoke in a televised address shortly after Trump's much-anticipated White House speech in which he "decertified" his support for the 2015 nuclear agreement, and left its fate in the hands of Congressional lawmakers.
"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.
He dismissed Trump's threat to "terminate" the landmark deal that Tehran signed with six world powers 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.
He criticised US involvement in wars from Vietnam to Afghanistan and Iraq, and highlighted the shooting down by a US naval vessel of an Iran Air passenger flight in 1988, which killed 290 people.
Many Iranians responded to Trump's speech on social media with the hashtag #NeverTrustUSA, with many highlighting the travel ban placed on Iranians earlier this year.
"The most disgusting part of Trump's speech was when he tried to show himself as sympathising with Iranians," wrote one Twitter user.
"Reminder: Not even 6 months have passed from the execution of visa ban for Iranians!" wrote another.
Response to sanctions
Trump stepped back from the sort of measures that would immediately torpedo the nuclear agreement, but he called for tougher sanctions on Iran's Revolutionary Guards and ballistic missile programme, and efforts to counter Iran's "destabilising" activities in the Middle East.
Iran's army spokesman Masoud Jazayeri responded by saying: "The armed forces will continue more determined than ever on its path of developing and enhancing its defence power," in quotes carried by state news agency IRNA.
Rouhani attacked Trump's characterisation of the Revolutionary Guards as a corrupt organisation propping up a "fanatical regime".
"Is the Iranian government a dictatorship... or is it the governments who are supported by the United States and still run their country on a tribal basis and have never seen an election in their country?" Rouhani said in a pointed reference to Iran's regional rival, Saudi Arabia.
Despite Trump's aggressive rhetoric, Rouhani said Iran for the time being remained committed to the nuclear agreement known as the Joint Comprehensive Plan of Action (JCPoA).
"We respect the JCPoA... so long as it remains in keeping with our national rights and interests," he said.
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.
"Are you upset with the slogans? Then stop your hostile policies," Rouhani said.
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