"I would certainly meet with Iran if they wanted to meet", Trump told reporters at a joint press conference with Italian Prime Minister Giuseppe Conte at the White House, caging his words by saying he is unsure if Iran is ready to talk but insisting that talks could be beneficial.
Some lower-ranking Iranian officials have responded by saying the path to direct discussions with Washington would have to include a USA return to the Joint Comprehensive Plan of Action, as the nuclear deal involving Iran, China, France, Russia, Britain, Germany, the US and the European Union was formally called.
Fresh off his meeting with Kim Jong Un, President Trump is talking about getting together with Iran's leaders "whenever they want" and "without preconditions". He recently took to Twitter to warn the country's leader not to threaten the U.S., promising severe consequences in future. If Trump thinks otherwise then (a) he's fooling himself and (b) he should set some preconditions through which Iran can demonstrate its potential willingness to abandon the nuclear program. I'm ready to meet any time they want to.
Bahram Ghasemi, Iran's Foreign Ministry spokesman, said Monday there was no possibility of dialogue, and that the USA had shown itself to be "totally unreliable".
Iran claims Trump tried on eight occasions to meet Rouhani at the United Nations General Assembly previous year.
Former IAEA chief Mohammed ElBaradei also told Trump, "You can not renege on a deal considered by all as a keystone, threaten the country, humiliate its leaders and then impulsively call for talks!"
In his first public remarks after the comment, Rouhani did not mention Trump at all, but instead stressed the need for the other nations involved in the nuclear deal to forge ahead with their pledges to try to salvage it.
Gulf states have accused Iran of backing Yemen's Houthi rebels with both money and weapons, though Iran has denied this.
Iran's semi-official ISNA news agency quoted Rouhani's political adviser Hamid Aboutalebi as saying that for talks to happen, the USA needs to rejoin the deal.
Given Iran's various centers of power and the skepticism about such a meeting on the part of Iranian Supreme Leader Ali Khamenei, the country's spiritual guide and most powerful man, it's very unlikely to happen.
The deputy speaker of Iran's parliament, Ali Motahari, said that to negotiate with Trump now "would be a humiliation". "I believe in meeting", Mr Trump said. The diplomacy that led to the Iran deal, for instance, would never even have taken off had it not been for Obama, in secret negotiations, accepting nuclear enrichment on Iranian soil.