The US has attacked Iran's leaders for "lying, cheating and deceiving", warning there will be "hell to pay" if it continues.
America's national security adviser, John Bolton, said: "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."
Speaking from New York during Donald Trump's visit to the UN, he added: "The murderous regime and its supporters will face significant consequences if they do not change their behaviour.
"Let my message today be clear: We are watching, and we will come after you."
Earlier in the day, Mr Trump had accused Iran's leaders of sowing "chaos, death and destruction" and "plundering the nation's resources to enrich themselves and to spread mayhem across the Middle East and far beyond".
US Secretary of State Mike Pompeo joined the verbal assault, describing Iran's leaders as "truly an outlaw regime".
Mr Pompeo also criticised Iran for its support of Syrian president Bashar Assad and Houthi rebels in Yemen.
He added: "There can be no question Iranian destructive activities are truly global in scope.
"It is therefore incumbent on every country to join our efforts to change the regime's lawless behaviour.
"The ongoing, multi-national, multi-continental nature of Iranian malign activity leaves no room for inaction or indecision."
The US has said it is determined to keep Iran isolated through sanctions, with the next round – due in November – to affect the country's oil industry, which accounts for 70% of its exports.
Mr Trump says that the sanctions, brought back after the US withdrew from the 2015 nuclear deal, will force Iran back to the negotiating table.
That looked unlikely, however, as Iran's president Hassan Rouhani attacked Mr Trump, describing the sanctions as "economic terrorism".
Mr Rouhani said: "The United States' understanding of international relations is authoritarian.
"In its estimation, might makes right.
"Its understanding of power, not of legal and legitimate authority, is reflected in bullying and imposition."
The 2015 deal, which included an agreement by Iran to curb its nuclear programme in exchange for relief from sanctions, was also signed by Britain, China, France, Germany, Russia and the European Union.
On Monday, those countries reaffirmed their commitment to the deal and announced plans for a "special purpose vehicle" to allow payments for Iranian imports and exports, including oil.
That angered Mr Pompeo, who described it as "one of the most counterproductive measures imaginable for regional and global peace and security".
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He added: "By sustaining revenues to the regime, you are solidifying Iran's ranking as the number one state sponsor of terror, enabling Iran's violent export of revolution and making the regime even richer while the Iranian people scrape by."
Mr Pompeo's words come as Donald Trump prepares to chair the UN Security Council for the first time on Wednesday.