At his swearing-in ceremony Mr Rouhani warned those present that America was trying to sabotage the nuclear accord.
Mr Trump’s aggression, said the President, may come to a sticky end: “Those who want to tear up the nuclear deal should know that they will be ripping up their own political life.”
The White House says Iran is complying with the deal but Mr Trump says Iran is violating its spirit. Last month the US state department announced new sanctions on the country.
The US says the sanctions relate to Iran’s missile programme and alleged support for terror groups but Tehran says they violate the nuclear deal.
Iran, its adversaries Saudi Arabia and the Donald Trump administration have demanded, should once again be shunned as a pariah state.
The US has imposed tough new sanctions and President Trump is threatening to pull the plug on the nuclear deal between the country and international powers which has been achieved through years of painstaking negotiations.