Speaking in his swear-in ceremony in the Iranian parliament, Rouhani criticized the US for threatening the implementation of the nuclear deal.
He said that the Islamic republic would remain committed to the international nuclear deal and would not violate the deal signed between Iran and the six major powers two years ago.
"However, Iran would not be silent in the face of US threats to the implementation of the deal," he said, adding that "Tehran would reciprocate every threatening move by Washington in this regard."
The Iranian President warned that "those who are thinking of tearing the accord into pieces, in actuality, would harm their political life."
Rouhani was alluding to the US President Donald Trump's comments on Iran's nuclear deal during his presidential campaign, as Trump repeatedly criticized the accord, calling it "the worst deal ever negotiated."
Observers say, Mogherini's presence in Tehran is a clear show of support for the Iranian president, who built his first four years in office on a policy of engagement with western nations.
Among other Western officials present were French Foreign Minister Jean-Yves Le Drian, State Secretary at the German Foreign Ministry Michael Roth, and British Minister of State Alistair Burt.
Two of Iran's neighbours Iraq and Afghanistan, where United States is embroiled in a bitter war, were represented at the highest level. President of Iraq Fuad Masum and Afghan President Ashraf Ghani were present along with Russian Deputy Prime Minister Dmitry Rogozin at the ianugral ceremony.
Rouhani told the gathering that the Iranian government has taken great steps to improve nation's health, adding that the level of education and health in Iran is better than many other countries.
Iran; however, is still facing big challenges including water shortage and unemployment, he noted.
Rouhani stressed the importance of a strong economy in the country and said the next government eyes economic reforms.
The Iranian president also said the Islamic Republic would continue to defend the oppressed nations throughout the world.
Rouhani said regional problems could be solved only through dialogue and cooperation and invited countries in the region to join political initiatives to end the crisis in Yemen.
He stressed the importance of increasing dialogue among governments and nations in order to repel the present "dangerous and complicated" threats.
"[Increasing] constructive interaction with world countries, deepening bonds with neighboring and regional countries and boosting the level of cooperation with friendly countries are not only a wise choice but a necessity," Rouhani said.
He warned of plots by foreign powers pursuing their self-interests in regional issues, saying they are creating chaos and instability in the Middle East.
Rouhani was re-elected in May and on Thursday was endorsed by Supreme Leader Ayatollah Ali Khamenei. He has two weeks to present his list of proposed ministers to the parliament.