Mr Trump vowed that re-imposed sanctions will be "in full force" and urged world powers to work with the United States to "ensure the Iranian regime changes its behavior and never acquires a nuclear bomb".
Without naming countries, the US President noted that "some nations are already violating UN sanctions" including illegal ship-to-ship transfers of oil and said compliance was "very, very important".
Moreover, German Foreign Minister Heiko Maas told reporters there was "strong unity" with Iran on minimizing the impact of United States sanctions.
In May, U.S. President Donald Trump withdrew from the Iran nuclear deal that his predecessor signed and started a monthslong process of reimposing U.S. sanctions that had been suspended under that agreement.
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Meanwhile, in the latest sign of the growing divide between Washington and its allies, the European Union's foreign policy chief said that the bloc was creating a new payment mechanism to allow countries to transact with Iran while avoiding USA sanctions.
Despite their best intentions and ongoing efforts to sustain benefits for Iran, remaining signatories to the 2015 nuclear deal - Europe, China and Russian Federation - have been unable to do enough to stop Iran's economy from suffering seemingly uncontrollable bleeding.
"As long as the deal serves our interests, we will remain in the pact", Iranian President Hassan Rouhani told reporters in NY.
"This is one of the most counterproductive measures imaginable for regional and global peace and security", he said.
Bolton said the United States will be "aggressive and unwavering" in enforcing its sanctions.
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Asked about those nations' back channel to continue economic relationships with Iran, Pompeo said: "To continue to create mechanisms to fund the world's largest state sponsor of terror is disastrous policy and I hope they will reconsider it".
Mogherini said Wednesday she believes the "Special Purpose Vehicle (SPV)", which is aimed at keeping trade with Tehran flowing while the USA sanctions are in place, will be established before November even though it is still at an initial stage now.
KELEMEN: And few companies will choose Iran over the U.S., Hook says.
Trump pulled out of the agreement in May, describing it as a "disaster" and quickly moving to reimpose sanctions on Iran.
The countries "welcomed practical proposals.to establish a Special Purpose Vehicle (SPV) to facilitate payments related to Iran's exports, including oil".
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Trump reimposed the sanctions after quitting the Iran accord in May, and called on U.S. allies to comply.