Khamenei, who has the last word on all major issues of state, formally endorsed Rouhani as president in a ceremony broadcast live on state television on Thursday, after the pragmatist romped to re-election on May 19.
As pertaining to global achievements in his first term in office, he referred to the signing of nuclear deal with six major world powers, namely Britain, China, France, Germany, Russia and the United States, which put an end to a decade-long dispute over the country's sensitive nuclear program.
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 United States sanctions passed last week.
Since assuming office in January this year, US President Donald Trump has adopted a hard line stance against Iran, which he accuses of sponsoring terrorism.
About 70 delegations from foreign countries and worldwide organisations have so far arrived in Tehran to attend the oath-taking ceremony of Hassan Rouhani as President of Iran.
Dozens of world dignitaries attended his inauguration, reflecting an easing in Iran's isolation since the nuclear deal.
After the ceremony, Rouhani addressed the participants that during the past four years in office, his government has achieved economic improvement in close interaction with the rest of the world.
GM slashed July rental vehicle sales, boosted commercial fleet
He said GM's decision to cut sales to low-profit rental auto fleets by 81 percent - or 11,200 vehicles - was a big factor. Mark LaNeve, Ford Motor Co .'s USA sales chief, said automakers have been preparing for lower sales this year.
Mogherini, who is the EU's high representative for foreign affairs and security policy, said for her part that the worldwide community shared interests with Iran in implementing the deal.
The law also imposed new sanctions on Russian Federation and North Korea.
Following his oath, Rouhani called for rule of law, freedom of speech and free access to information in Iran.
Chung also met Iranian President Hassan Rouhani, sharing ideas on expanding exchanges and joining forces for peace on the Korean Peninsula.
But the Europeans do oppose Iran's recent missile tests, with the French foreign ministry stating on Thursday that they "contradict" UN Resolution 2231 which oversees the nuclear deal, and "constitute a potential threat to stability and security in the region".
Rouhani, 69, was decisively re-elected in May with around 57% of the vote.
Amnesty International recently released a 94-page report entitled "Caught in a Web of Repression - Iran Human Rights Defenders Under Attack", which detailed the situation for those in Iran who stand up for human rights against the regime.
Afghan experts said they believe that Iran should thank Afghanistan for benefiting from its water resources in the course of history.