The European Union has sought to salvage the nuclear deal and provide legal cover for its companies to continue operating in Iran. "I am asking for WORLD PEACE, nothing less".
Rouhani, who has denounced Trump's decision to quit the accord, is expected to address his nation later on Monday.
The sanctions Mr. Trump reimposed at midnight were lifted by former President Barack Obama as part of the 2015 Iran deal. The US wasn't trading with Iran in the first place, so Iran isn't actually losing anything on that front.
China, Russia and Turkey have already indicated that they would not comply with the unilateral U.S. sanctions.
They are also created to scare off foreign investors in the Iranian automotive industry, something that appears to have been achieved already.
"The United States is fully committed to enforcing all of our sanctions, and we will work closely with nations conducting business with Iran to ensure complete compliance".
One of the officials said that almost 100 global firms have announced their intention to leave the Iranian market, particularly in the energy and finance sectors.
The stiff economic sanctions ratchet up pressure on the Islamic Republic despite statements of deep dismay from European allies, three months after Trump pulled the US out of the worldwide accord limiting Iran's nuclear activities.
Iran is also taking solace in the fact that most of the world strongly opposes Trump's policy, with China, India and Turkey all saying they are unwilling to substantially cut purchases from Iran when the United States reimposes sanctions on the energy sector on November 5.
The EU foreign affairs chief Federica Mogherini said that the EU would pass a "blocking statute" on Tuesday to nullify United States legal action against European companies in connection with Iran.
In defiance of the USA, the European Union urged its companies to continue and even bolster trade with Tehran, despite American threats of sanctions against them for doing business.
Trump decided this year to pull out of the agreement, ignoring pleas from the other world powers that had co-sponsored the deal, including Washington's main European allies Britain, France and Germany, as well as Russian Federation and China.
Some companies already suspended trade in anticipation of the new sanctions.
The measure is part of a broader European Commission response, known as the "blocking statute", that also allows the firms to recover damages arising from U.S. extra-territorial sanctions.
The US was an original signatory to the agreement with Iran, along with Britain, France, Germany, Russia, China and the EU.
Mr Trump has called the deal "one-sided", "disastrous" and the "worst I've ever seen". Iranian President Hassan Rouhani struck a hard line Monday as the USA restored some sanctions that had been lifted under the 2015 nuclear deal. Energy dependent Japan and Germany both are reluctant to cut business relations with Iran.