"I am amazed at the interpretations of Mr. Trump, vis-a-vis terrorism," Rouhani told "Fox News Sunday" anchor Chris Wallace.
"Today, America, unfortunately, is the supporter of terrorism in our region -- and wherever America has gone, terrorism has expanded in the wake."
Rouhani pointed to U.S. military involvement in Syria without the permission of President Bashar al-Assad as an example of what he considered to be such American 'terrorism.'
"The country that is present and flying over the air space of and bombarding the soil of the country of Syria without permission of the government is the United States of America."
Wallace had asked Rouhani about Trump's U.N. speech earlier Tuesday, in which he referenced Iran's "blood lust" and "fanatical quest for nuclear weapons" when the Iranian leader gave that response.
Earlier this month, Rouhani told the British Parliament in a speech that Tehran would continue to deflect Washington's overtures for a bilateral meeting.
“There have been a lot of offers for talks but our answer will always be negative,” he said, as the BBC reported.
However, Iran would be open to having multilateral talks if the U.S. agreed to scrap its economic penalties targeting Iran, Rouhani noted.
In 2015, the P5+1 -- the U.S., the U.K., China, France and Russia, plus Germany -- penned a nuclear pact with Iran and the European Union. President Trump announced last year that the United States was leaving the Joint Comprehensive Plan of Action, which he called "the worst deal ever” for America, maintaining that Iran was violating the deal.
Fox News' Chris Wallace and Melissa Leon contributed to this report.