"Talks with the U.S. would have been right had the USA not withdrawn from the JCPOA and imposed sanctions on Iran", Ali Motahhari said, according to Iran's state-run IRNA news outlet. One of the earliest responses was issued by an aide to President Rouhani, who said on Tuesday that the USA would have to return to the internationally-backed nuclear deal and stop new sanctions against Iran if it wants negotiations with Tehran.
"Today we are at a very critical point in history regarding the nuclear deal, and Europe's transparent measures to compensate for the United States' unlawful withdrawal from it are very important for the Iranian nation", Rouhani said after talks with new British Ambassador Rob Macaire.
Asked if his call for $25 billion for a border wall is a "red line", Trump said, "I have no red line, unlike President Obama" - a reference to his predecessor's infamous statement about chemical weapons use in Syria.
Meeting his Iranian adversaries, Trump said, would be "good for the country, good for them, good for us and good for the world".
"I don't know if they're ready to meet - they are having a hard time right now".
Mr Trump's abrupt change in tone also echoes the run-up to his meeting with North Korean leader Kim Jong-un, another diplomatic first, which took place after the two leaders had previously traded insults and threats.
In Washington, a senior State Department official said Secretary of State Mike Pompeo had no plans to meet with Iranian Foreign Minister Mohammad Javad Zarif if they both participate at an Asian security forum in Singapore later this week. "There's nothing wrong with meeting", Trump said.
Heshmatollah Falahatpisheh, who heads the parliamentary committee on national security and foreign policy, suggested a USA return to the nuclear deal would be needed before Tehran could think of negotiating, while Kamal Kharrazi, the head of Iran's Strategic Council on Foreign Relations, said Trump's offer was worthless.
Iran has reacted coolly to the offer, but a former adviser to the country's supreme leader said Tuesday that Tehran should not reject a sit-down out of hand.More news: Johnny Manziel traded from one Canadian Football League team to another
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"Iran came to the table to negotiate the  nuclear deal after years of sustained pressure from the U.S., Britain, France, Germany, Russia and China", Kenyon says.
In a panic to stop the damage as USA sanctions are set to be reimposed starting next week, the Central Bank of Iran announced plans to move forward with its own cryptocurrency on Monday.
That included a searing all-caps tweet earlier this month after what seemed like a mundane warning from Iran about a possible armed conflict.
The Majlis deputy speaker said the situation is not right for negotiations "because it will be accompanied by disgrace and humiliation". Brian Hook, the State Department's director of policy planning, said on July 2 that more than 50 global firms have already announced their plans to leave Iran, "particularly in the energy and finance sectors".
Regime change should be our goal.
Trump condemned the deal in part because it did not cover Iran's ballistic missile program and involvement in Middle East conflicts.
The head of the powerful Revolutionary Guards equally dismissed Trump's tentative offer, saying the Islamic Republic was not North Korea.
But Iran's currency, the rial, has been in a freefall - dropping 18 percent just in the past two days.