On Thursday, Rouhani vowed to focus on economic growth of the country as he was endorsed by the Iranian Supreme Leader as Iranian president for his second term.
Rouhani's speech took place soon after US President Donald Trump signed the bill passed by Congress on new sanctions against three countries, including Iran.
During their Friday meeting, Zarif held talks with Ghana's Vice-President Mahamudu Bawumia, who is in Tehran to attend President Hassan Rouhani's inauguration on Saturday.
Dozens of world dignitaries attended his inauguration, reflecting an easing in Iran's isolation since the nuclear deal.
On Thursday, Iran denounced the recent endorsement of new sanctions against the Islamic republic by the US president, saying that it violates nuclear deal.
The deal has seen European countries flocking back to invest in oil-rich Iran, with the French energy giant Total agreeing to develop a new phase of the South Pars natural gas field, the world's largest.
Mogherini, who is the EU's high representative for foreign affairs and security policy, said for her part that the global community shared interests with Iran in implementing the deal.
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. "For example, improvements in specific human rights, which we didn't yet do", said Becerra, referencing the nuclear agreement of 2015, which gives the European Union leverage to force this human rights issue front and center.
North Korea has rejected calls for Iran-style nuclear talks, noting its situation is different from that of Iran.
"The actions of the U.S. regarding the implementation show that the United States can't be trusted", Rouhani said.
Separately, Russian state media are reporting Russia and Iran have agreed to strengthen military, technical and technological cooperation following the new U.S. sanctions.
Much of Rouhani's popularity has been built on his promise of greater civil liberties, including more rights for women, but Iran has still had only one female cabinet member since the 1979 revolution - ironically under hardliner Mahmoud Ahmadinejad.