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(CNN) —  

US national security adviser John Bolton issued a stark warning to Iran Tuesday, demanding changes in Tehran’s behavior and threatening there will be “hell to pay” if they don’t happen.

“According to the mullahs in Tehran, we are ‘the Great Satan,’ lord of the underworld, master of the raging inferno,” Bolton said in New York Tuesday. “So, I might imagine they would take me seriously when I assure them today: If you cross us, our allies, or our partners; if you harm our citizens; if you continue to lie, cheat, and deceive, yes, there will indeed be hell to pay,” Bolton said at the United Against Nuclear Iran Summit, held on the margins of the UN General Assembly.

Bolton’s comments were part of a full-court press by Trump administration officials attending the UN General Assembly in New York to condemn Iran and rally other countries to join in an effort to pressure the country into changing its behavior.

A unified message

President Donald Trump called out Iran in his remarks to the General Assembly. Secretary of State Mike Pompeo released a report that the State Department said detailed Iran’s malign behavior. Other US officials briefed reporters on Iran and its activities. The message was clear and unified: Iran must change or deal with the US, and the world should join Washington in this endeavor.

Iran pushed back, accusing the Trump administration of a “might is right” authoritarian streak and of violating international law.

“The United States’ understanding of international relations is authoritarian,” said President Hassan Rouhani said in his address to the General Assembly Tuesday. “In its estimation, might makes right. Its understanding of power, not of legal and legitimate authority, is reflected in bullying and imposition.”

The US messaging underscored tensions with Europe, as the US officials criticized EU steps to maintain the 2015 Iran nuclear pact, which eased sanctions on Tehran in exchange for curbs on its nuclear program, and for the EU’s attempts to find ways to help Iran continue to trade.

The US officials said sanctions set to hit in November on those who buy Iranian energy supplies will be followed by further punitive steps meant to hurt and isolate Tehran.

“It is incumbent on every country to join our efforts to change the regime’s lawless behavior,” Pompeo said, speaking at the conference. “The ongoing, multinational, multicontinental behavior of Iranian malign activity leaves no room for indecision,” he said. “This is among the President’s top diplomatic priorities.”

Rouhani said the US, with its sanctions threats, “pressures other countries to violate the nuclear accord. And more dangerously,” was threatening countries and international organizations with punishment if they adhered to the international agreement.

“It is the first time in the history of the United Nations that such ‘a general invitation to violation of law’ has been coupled with ‘threatening law-abiders with punishment,’ ” Rouhani said.

The Iran nuclear deal, which Bolton called “the worst diplomatic debacle in American history,” has become a bone of contention between the US and Europe, which continues to defend it. On Monday, the EU, China and Russia, all of which remain signatories to the deal, announced a mechanism to help Iran continue to engage in international trade and avoid US efforts to cut off Tehran’s financial flows.

Both Bolton and Pompeo expressed their dismay and anger.

“The European Union is strong on rhetoric and weak on follow through,” Bolton said, adding “we will be watching the development of this structure that does not exist yet and has no target date to be created.”

“We do not intend to allow our sanctions to be evaded by Europe or anybody else,” he said.

Pompeo called the move “counterproductive,” saying he “was disturbed” and “deeply disappointed” to hear of the mechanism announced Monday night by Federica Mogherini, the EU’s high representative for foreign affairs.

Pompeo called the “special purpose vehicle” that will facilitate trade of goods and oil “one of the most counterproductive measures for regional and global peace and security” and accused the EU of “enabling Iran’s violent export of revolution.”

He also decried the move in light of “the litany of Iranian-backed terrorist activity inside of Europe.”

Referring to Iran’s Revolutionary Guard Corps, which has broad economic interests in the country and region, Pompeo said “I imagine the corrupt ayatollahs and the IRGC were laughing this morning.”

“How can any nation that claims to sympathize with the people of Iran keep sustaining trading relationships with lawless and oppressive ayatollahs?” Pompeo said.

Bolton said the US would be equally hard on Iran’s “enablers.”

“The United States is not naive,” Bolton said. “We will not be duped, cheated or intimidated. The days of impunity for Tehran and its enablers are over. The murderous regime and its supporters will face significant consequences if they do not change their behavior. Let my message today be clear: We are watching, and we will come after you.”

Bolton said that the Trump administration is also implementing measures to specifically target Iranian general Qasem Soleimani, who heads the Revolutionary Guard Corps.

“The Trump administration has launched a pressure campaign to counter Soleimani’s insidious design,” Bolton said.

’We will not stop’

Bolton said that “US intelligence clearly shows Iran is actively developing more accurate and capable missile systems” and that Iran continues to use intermediaries and front companies in Asia and Russia to obtain missile components.

Bolton also demanded the release of American and Western citizens held in Iran.

“Robert Levinson, whose family I met last week, went missing in Iran over 11 years ago,” Bolton said, naming an American former FBI agent.

“Siamak Namazi and Xiyue Wang are wrongfully detained in Iran,” Bolton added, naming a business consultant and an academic. “Numerous other American and Western citizens are held captive by the regime. This shameful and barbaric practice must end, and Iran must return our Americans and other innocent civilians at once.”

“The ayatollahs have a choice to make. We have laid out a path toward a bright and prosperous future for all of Iran, one that is worthy of the Iranian people, who have long suffered under the regime’s tyrannical rule,” he said.

“We will not stop pressuring Iran to stop its destabilizing behavior,” he said.