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"They want to meet, I'll meet. Anytime they want," Trump said. The president's comments came amid escalating tension between the U.S. and Iran. Earlier this month, Trump threatened Rouhani in an all-caps post on Twitter that called out the Iranian leader by name.
A meeting with Rouhani would be "good for the country, good for them, good for us, and good for the world," the U.S. president said.
It's not clear whether Iran would accept any proposed meeting, particularly given the threats the president has issued. In July, Rouhani's chief of staff, Mahmoud Vaezi, said that Trump had asked eight times for a meeting with Rouhani, and was rejected each time, according to a state-run news agency.
Asked by CNBC on Monday about reports that Iran had rebuffed the administration's overtures, Secretary of State Mike Pompeo said he would not speak about private conversations that may or may not have taken place.
Pompeo said he is on board with Trump meeting Iran's leadership, but he outlined several conditions for that meeting.
Trump withdrew the United States from the 2015 Iran nuclear deal in May after failing to marshal international support for a tougher approach to the Middle Eastern country. The European Union is trying to salvage the accord, which placed limits on Iran's nuclear program in exchange for sanctions relief.
"If we could work something out that's meaningful, not the waste of paper that the other deal was, I would certainly be willing to meet," Trump said Monday, pointing out that it would be good for the United States, Iran and the world.
In pulling out of the agreement, the Trump administration restored wide-ranging sanctions on Iran. His administration is pushing oil buyers to stop purchasing crude from Iran, the world's fifth largest oil producer, by Nov. 4.
The ultimatum — cut Iranian crude imports to zero or face U.S. sanctions — has ratcheted up tension in recent weeks. Iran has threatened to shut down the world's busiest sea lane for oil shipments. Its allies in Yemen, the Houthi rebels, forced Saudi Arabia to suspend oil shipments through another critical chokepoint in the Red Sea after they attacked Saudi tankers.
Trump, whose White House has stylized him as the "ultimate negotiator and dealmaker," stressed the high stakes of any potential meeting with Rouhani.
"Speaking to other people, especially when you're talking about potentials of war, and death, and famine, and lots of other things — you meet," he said. "There's nothing wrong with meeting."
"As you know, with Chairman Kim we haven't had a missile fired in nine months, we got our prisoners back, so many things have happened so positive," the president said Monday. Trump said his summit with Putin was a "great meeting in terms of the future."
Vaezi has warned against making comparisons between North Korea and Iran, according to the July article.
"The characteristic of this Establishment and [Iranian] people is that they will not yield to pressure," he said at the time. "Trump should know that Iran and its people are different from North Korea and its people."
The president's remarks Monday came during a joint news conference with Italian Prime Minister Giuseppe Conte. The two met earlier in the day in private.
— Reuters contributed to this article.