In an interview with NBC's "Meet the Press" Sunday, Secretary of State Mike Pompeo said the president is willing to speak with President Hassan Rouhani.
President Trump and his Iranian counterpart will offer duelling addresses to the United Nations today after threats of new U.S. sanctions and a claim from the Supreme Leader that American allies funded an attack on a Revolutionary Guard parade on Saturday.
Both countries' presidents were due to attend the U.N. General Assembly in NY where Trump is scheduled to address the gathering at 10:15 a.m. (1415 GMT).
The idea is to circumvent US sanctions due to be restored in November under which Washington can cut off from the USA financial system any bank that facilitates an oil transaction with Iran.
"Maybe someday in the future", he tweeted. The European Union agreed on Monday to come up with a plan to circumvent USA sanctions on Iran.
President Trump said Tuesday he "has no plans" to meet with Iran's president until the Iranians "change their tune" on destabilizing the Middle East.
"The evil and adventurous American president has focused on an economic war and cruel sanctions to deviate the Iranian nation from the revolutionary values and its national interests", the corps said in a statement published on state media and reported by the Reuters news agency.
Trump withdrew from the nuclear deal in May, to the dismay of European allies, Russian Federation and China which had invested years in negotiations to achieve a milestone agreement on keeping Iran's nuclear ambitions in check.
Alireza Miryousefi, spokesman for Iran's United Nations mission, told Reuters that Iran has not requested a meeting with Trump.
The other parties to the 2015 nuclear deal - Britain, France, Germany, China, Russia, and Iran - are eager to keep alive the deal, known as the Joint Comprehensive Plan of Action, while hoping to avoid United States punishments for not complying with the sanctions. "I am sure he is an absolutely lovely man!" he said.
Rouhani's comments come a day after Saudi Arabia and its biggest oil-producer ally outside the group, Russia, ruled an immediate hike in crude output, pushing back on President Donald Trump's call to cool the oil market.
Quashing the current pact would come at a political cost for the Iranian president, who championed the deal with the supreme leader's guarded backing and who could lose support from European allies.
Since Trump came to power, promising that the world's most powerful country would follow an unashamedly "America First" foreign policy, there have been growing fears about the USA commitment to multilateral institutions such as the United Nations.
The United Kingdom, France, and Germany have signed an agreement with Russian Federation and China to circumvent USA sanctions on Iran.
European Union foreign policy chief Federica Mogherini announced the plan after talks at the United Nations with the remaining members of the accord - Britain, China, France, Germany, Russia.