Trump earlier in the day said he once again would extend US sanctions relief for Iran, as required under the deal in exchange for curbs on Iran's nuclear activities, but he intends to pull the United States out the agreement unless it is strengthened within months.
USA officials said the new sanctions were for human-rights abuses by the Iranian regime during its response to civil protests, and for weapons proliferation.
U.S. regulations require the president to endorse JCPOA every 90 days and extend waivers of economic sanctions against Iran every 120 days. Trump wants the bans to be permanent.
"They should join us in constraining Iran's missile development and stopping its proliferation of missiles, especially to Yemen", he said. These restrictions were levied because of Iran's human rights violations, support of terrorism, and pursuit of a ballistic missile program.
Iran has vowed to fight back against sanctions imposed on its judiciary head by the U.S., as President Donald Trump steps up efforts to "fix" a nuclear deal between Tehran and major powers.
Foreign financial institutions or individuals could also face sanctions for doing business with those blacklisted, the US Treasury added.
He was among those calling for a crackdown following a recent spate of anti-government protests across Iran. Had he sanctioned the bank, there was speculation that Iran would view the deal as effectively abrogated.
"The Islamic Republic of Iran stresses clearly that it will not take any measures beyond its commitment to the JCPOA, nor will it accept changes to this agreement now or any time in the future".
The EU and United Kingdom also acknowledged Trump's announcement, but said they would not decide on a course of action until discussing it further with the deal's European signatories.
Iran's Foreign Minister Mohammad Javad Zarif said it was a "desperate attempt" to undermine a "solid" deal.Germany said it would continue to call for the deal's full implementation and would consult on a "common way forward" with the United Kingdom and France. These areas fall outside the scope of the nuclear deal. The accord bars Iran from enriching uranium beyond low levels of 3.5 percent, which can be used to power reactors.
The president revoked a 2012 presidential executive order that slapped sanctions on companies that purchased oil from Iran, conducted transactions with its national oil company or helped Iran buy previous metals and US banknotes. Trump wants them to continue indefinitely so that the United States can rapidly resume sanctions if Iran is ever found to be cheating.
Iran's Foreign Minister Mohammad Javad Zarif describe Trump's decision as "desperate attempt" to "undermine" the deal.
The nuclear deal between Iran and six world powers - the US, UK, Russia, France, China, and Germany calls upon Iran not to undertake any activity related to ballistic missiles created to be capable of delivering nuclear weapons, including launches using such ballistic missile technology.
The prospect of a U.S. withdrawal from the Iran deal "will deliver a very serious blow to the whole system of worldwide agreements and to the enhancing of the nuclear nonproliferation regime", he added.
Whether the United States and European partners will be able to agree on a supplemental deal by May that strengthens the nuclear agreement is far from clear. Work already has begun on this front.
The president once again waived economic sanctions that were explicitly tied to Iran's nuclear program and were eased under the accord.
Robert Malley, who worked on the National Security Council under former President Barack Obama, said, "In a nutshell, he's saying, 'Kill the deal with me, or we'll kill it alone'".
Zarif said, "Such words stream out of the mouth of an individual who deems himself the [chief] executive of a country; that culture, that orientation and approach is an obstacle in the way of a paradigm of inclusive dialogue".
Russian Deputy Foreign Minister Sergei Ryabkov called Trump's remarks "extremely negative", RIA state news agency reported.