Mr Rouhani derided the sanctions which the Trump administration announced against Supreme Leader Ali Khamenei as “outrageous and idiotic” during a nationwide broadcast on the state television.
The Iranian president said the supreme leader would not be crippled by the sanctions because he does not have assets abroad, saying the move betrayed America’s desperation.
“The White House actions mean it is mentally retarded,” Mr Rouhani said.
Mr Rouhani has long maintained a measured tone towards Mr Trump, leaving his officials to make derogatory remarks on foreign policy matters.
“Tehran’s strategic patience does not mean we have fear,” Mr Rouhani added.
Mr Trump announced new sanctions against Mr Khamenei and other top Iranian officials on Monday, hoping it would tighten pressure on Iran for shooting down an unmanned U.S. drone last week.
Senior military figures in Iran were those largely targeted in the new sanctions that hindered their access to any financial assets under U.S. jurisdiction. Further sanctions aimed at Iranian foreign minister Mohammad Zarif would be announced this week, the U.S. said.
Mr Zarif and other senior Iranian figures have dismissed the sanctions as inconsequential and infantile, saying it would shut down all avenues for diplomatic talks to end their prolonged conflict.