Addressing world leaders at the U.N. General Assembly, Rouhani accused the Trump administration of violating the rules of international law and "state obligations" from the Obama administration by withdrawing from the 2015 nuclear deal that Iran signed with the U.S. and five other major powers.

"On what basis and criteria can we enter into an agreement with an administration misbehaving such as this?" Rouhani asked. "It is ironic that the U.S. government does not even conceal its plan for overthrowing the same government it invites to talks."

Rouhani invited the U.S. to come back to negotiations within the U.N. Security Council, which endorsed the nuclear deal. There, he said, both sides can listen to each other.

"Beginning the dialogue starts with ending threats and unjust sanctions that negate the principles of ethics and international law," he said. "What Iran says is clear: no war, no sanctions, no threats, no bullying. Just acting according to the law and the fulfillment of obligations."

In remarks released while Rouhani was still talking, U.S. National Security Adviser John Bolton doubled down on the decision to withdraw from the deal, calling it "the worst diplomatic debacle in American history." He echoed Trump's strong language and used blunt words to dismiss any entreaties from Tehran.

"According to the mullahs in Tehran, we are 'the Great Satan,' lord of the underworld, master of the raging inferno," Bolton said in remarks prepared for delivery at a New York meeting convened to oppose Iran's nuclear ambitions.

"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.

The capitalizations were included in the text of the quotes released to journalists.

In his General Assembly speech, Rouhani targeted Trump in language if not directly in name.

"The United States' understanding of international relations is authoritarian," he said. "In its estimation, might makes right."

Rouhani condemned "recklessness and disregard of some states for international values and institutions." He laid into leaders who believe they can "ride public sentiments and gain popular support through the fomenting of extremist nationalism and racism" and through what he called "xenophobic tendencies resembling a Nazi disposition."

Trump, in his own speech, said Americans "reject the ideology of globalism" in favor of what he called "the doctrine of patriotism." He also blasted what he called Iran's "corrupt dictatorship" and said its leaders "sow chaos, death and destruction" and "spread mayhem across the Middle East and far beyond."

The Iranian president took a dig at Trump's opposition to nations working together, adding a personal twist.

"Confronting multilateralism is not a sign of strength. Rather, it is a symptom of the weakness of intellect. It betrays an inability in understanding a complex and interconnected world." Rouhani said.

Rouhani accused the U.S. of pressuring other countries to violate the nuclear agreement and threatening to punish those who comply with the Security Council resolution endorsing it. He said Iran appreciates the European Union, Russia and China for supporting its implementation.

Foreign ministers from the five remaining signatories to the nuclear deal — Britain, France, Germany, Russia and China — agreed at a meeting with Iran's foreign minister Monday to establish a financial facility in the European Union to facilitate payments for Iranian imports and exports including oil. That was sought by Tehran to counter U.S. sanctions.

U.S. Secretary of State Mike Pompeo harshly criticized those countries for attempting to subvert U.S. sanctions, telling an anti-Iran meeting: "This is one of the most counterproductive measures imaginable for regional and global peace and security."

Trump's administration reinstated sanctions on Iran after pulling Washington out of the 2015 nuclear deal. The administration has accused Iran of promoting international terrorism.

In remarks earlier Tuesday, Trump predicted that the pressure from renewed sanctions would force Iran back to the table to negotiate. But Rouhani noted that Iranians have endured sanctions before and cannot be "brought to the negotiating table by force."

The Iranian president said his country will remain a link between East and West, noting that it fought Iraq's ruling party before Saddam Hussein invaded Kuwait in 1990, battled the Taliban and al-Qaida before 9/11 and was opposing the Islamic State extremist group before its attacks in Europe.

"Appreciate these historical realities about Iran," Rouhani told leaders at the end of his speech. "Quit imposing sanctions and end extremism. The world will not have a better friend than Iran, if peace is what you seek."