Meeting with Mogherini before the ceremony in parliament, Rouhani called for greater efforts to uphold the 2015 nuclear deal struck by Tehran and world powers in the face of new United States sanctions passed last week.
After Rouhani's re-election in May, she took to Twitter to fulsomely praise Iran's electoral process, declaring, "Iranians passionately took part in the political life of their country". "Now in Iran, there is a growing debate if these sanctions violate [the nuclear deal] or not".
High Representative Mogherini is in Tehran to attend the inaugural ceremony of Iranian President Hassan Rouhani.
Last month the United States announced new sanctions against entities and individuals with ties to Iran, a day after certifying the Iranian government's compliance with the nuclear agreement.
"Today, Iranians have learned how to take measures concerning the enemy's plots and Iranian officials know how to deal with the enemy".
The EU will safeguard the nuclear deal "with determination", Mogherini said, according to the official Islamic Republic News Agency.
Earlier on Saturday, Rouhani discussed bilateral relations with European Union foreign policy chief, Federica Mogherini, Iraqi President Fuad Masum, Afghan President Ashraf Ghani and Speaker of South Korea's National Assembly Chung Sye-kyun.
Following his oath, Rouhani called for rule of law, freedom of speech and free access to information in Iran.
Iran says it has no such warheads and no such missiles and has put its nuclear program under enhanced worldwide monitoring as part of the nuclear deal.
Rouhani, 69, was decisively re-elected in May with around 57% of the vote.
"The nuclear deal is a sign of Iran's goodwill on the worldwide stage", he added.
Rouhani stressed the importance of a strong economy in the country and said the next government eyes economic reforms.
However, his inauguration came less than 24 hours after fresh sanctions were imposed by US President Donald Trump, who has threatened to tear up the nuclear deal entirely.
Rouhani's own supporters have expressed concern over his inability to include women as ministers in his new cabinet because of pressure from religious hardliners.