The swearing-in ceremony comes two days after Supreme Leader Ayatollah Ali Khamenei endorsed Rouhani's presidency for a second four-year term.
Meeting Mogherini before the ceremony in parliament, Rouhani called for greater efforts to uphold the 2015 nuclear deal struck by Iran and world powers despite the fresh U.S. sanctions passed last week.
Iran's President Hassan Rouhani was sworn in for a second term on Saturday and he promptly warned the USA against tearing up the nuclear deal reached with Barack Obama.
He said that the Islamic republic would remain committed to the worldwide nuclear deal and would not violate the deal signed two years ago.
Drawing attention to the fast growing rate of executions in Iran under Rouhani, Alejo Vidal-Quadras - a former president of the European parliament - said that the decision of the EU's high representative for foreign policy to attend Rouhani's inauguration was "morally and politically unconscionable".
"Overcoming unsafe threats and complicated developments in the current state of flux is not possible, except through increased contacts and interaction and establishment of dialogue with governments and nations".
Pakistani parliament to elect new PM on Tuesday
The opposition could also field a candidate for the premiership, though the nominee has little chance of getting sufficient votes. It was unclear who will be appointed to take over the post till the next general elections, scheduled for 2018.
Iranian officials say they have prepared a 16-point document for how they will respond to the new sanctions, without giving details.
Among the guests were European Union foreign policy chief Federica Mogherini, who has vowed to continue building ties with Iran despite mounting pressure from the United States to keep the Islamic republic isolated.
In the May 19 polls, Rouhani clinched 23.5 million votes out of some 41 million ballots cast, beating out hardline rival Ebrahim Raisi, who secured 38.5 percent of the vote.
Rouhani stressed the importance of a strong economy in the country and said the next government eyes economic reforms.
The state department announcement came a day after the Trump administration certified that Tehran was complying with its nuclear deal obligations.
Trump, who during his election campaign previous year called 2015's nuclear agreement "the worst deal ever", signed new sanctions into law on Wednesday, along with measures against Russian Federation and North Korea. Officials from over 90 countries attended the event.
Rouhani also called America "a country that isn't reliable when it comes to global issues".
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