Mr Trump has described the landmark agreement as the "worst deal ever".
Nevertheless, his statement added, the Treasury Department will apply new targeted sanctions on individuals and firms helping Iran's banned ballistic missile program.
Many Iranians have expressed their disappointment at the fact that the economic boom they expected post-sanctions relief has not yet come, suggesting a growing impatience among the Iranian population with Rouhani's continued optimistic talk of the nuclear accords.
Mark Dubowitz, an Iran expert and head of the Washington-based Foundation for Defense of Democracies, which advocates for a tough USA position on Iran, said the latest steps were part of a "much more comprehensive strategy to use all instruments of American power to roll back Iranian regional aggression" and to "rectify what the administration sees as a deeply flawed nuclear deal".
I can understand why the Trump administration might want to maintain the nuclear deal until it gets all its ducks in a row on Iran.
Iran and major powers led by the USA made a deal in 2015 to curb Tehran's nuclear ambitions in exchange for easing economic sanctions.
As contentious as the 2015 Iran nuclear deal is in the US, it has been even more divisive in Iran. In the meantime, Jones said, the USA will keep implementing the deal, including the sanctions relief.
The decision came just before a Friday presidential election in Iran, in which moderate President Hassan Rouhani is fighting for a second term against hard-line cleric Ebrahim Raisi, who has called for a much tougher stance against the West.More news: 70th Cannes film festival jury arrive ahead of opening day
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It is very likely that Trump's tactic of keeping old sanctions at bay while imposing new ones is meant to demolish any accusation that he is softening his position on Iran.
China lodges an official protest with the United States over new USA sanctions on Iran that target a Chinese business tied to Tehran's ballistic missile program.
The administration of US President Donald Trump yesterday chose to stick by a nuclear deal between Iran and world powers and continue waiving sanctions related to its atomic activities.
"We urge our partners around the world to join us in calling out individuals and entities who violate worldwide sanctions targeting Iran's human rights abuses", Jones said. The US said his network helped produce electronics, such as missile guidance for Iran's program.
The ministry in a statement said Iran's right to strengthen its military capabilities is not a violation of the country's nuclear agreement with world powers.
The State Department also released a new report criticizing Iran for human rights abuses.
Every 90 days, the USA president must certify for Congress that Iran is fully compliant with the JCPOA to ensure that the economic sanctions can continue to be waivered. Critics in Iran have complained that the deal has not produced sufficient economic benefits, and critics in the United States say it rewarded Iran without long-term guarantees to prevent Tehran from securing nuclear weapons.