President Rouhani, who had a landslide victory in May this year will be sworn in for his second term in office.
Iran's Interior Ministry has chose to raise security level at the Parliament to "critical" during the inaugural ceremony.
Trump has expressed skepticism about the nuclear agreement, which significantly reduced the scope of Iran's nuclear program in exchange for lifting sanctions, and has sought other ways to keep the pressure on Tehran.
The new law provides Congress with more authority over the Russian sanctions program by requiring the President to submit a report to Congress whenever he proposes to make certain changes to US sanctions on Russia.
A high-level delegation of Hamas leaders touched down in Tehran on Friday to pay respects at the swearing-in ceremony of Iran's President Hassan Rouhani, a further sign of rapprochement between the two after falling out over the Syrian civil war.
Dozens of world dignitaries attended Mr Rouhani's inauguration at Iran's parliament, reflecting an easing in Iran's isolation since the nuclear deal.
Iran and the P5+1 countries, namely the US, Russia, China, France, Britain and Germany inked the nuclear deal, officially called the Joint Comprehensive Plan of Action, on July 2015 to end United Nations sanctions against the Islamic state, which was being accused of developing nuclear missiles. The bill aims to stop anyone who's dealt with the Iranian ballistic missile program from entering the US, and blocks those associated with the program from buying or selling property held in the U.S.
South Korea's parliamentary leader has urged North Korea to learn lessons from the Iran nuclear agreement and return to nuclear talks.
He will be sworn-in as the president on Saturday, according to Reuters.
Zarif described the United States move as a violation of the nuclear deal's text, and said, "Trump tries to breach the deal with Iran paying the costs, but Europe needs to be alert in this regard".
"The main ministers are very likely to stay in place", said Henry Smith, Iran analyst with consultancy Control Risks, told AFP. French energy giant Total defied USA pressure in July by signing a multi-billion-dollar gas deal with Iran.
"Iran will never be the first country to start violating" the accord, Rouhani, 68, said in the Iranian parliament, speaking to officials including European Union foreign policy chief Federica Mogherini. It also imposes mandatory sanctions on the already-sanctioned Iranian Revolutionary Guard Corps ("IRGC") and the IRGC-Quds Force (and their officials, agents, and affiliates) for their support for worldwide terrorism.
Among Iranians, the real attention was on who would be named to Rouhani's new cabinet.