On Monday Trump said he could meet the Iranians with "no preconditions", adding that "if they want to meet, I'll meet anytime they want".
Mr. Trump also was criticized for meeting with North Korean leader Kim Jong-un and Russian President Vladimir Putin.
Foreign Minister Javad Zarif tweeted in response, "COLOR US UNIMPRESSED: The world heard even harsher bluster a few months ago".
Analysts do not expect a Trump-Rouhani meeting anytime soon, pointing out that Trump has, for some time, been seeking to meet Rouhani directly without success.
"Talks with the U.S. would have been right had the USA not withdrawn from the JCPOA and imposed sanctions on Iran", Ali Motahhari said, according to Iran's state-run IRNA news outlet.
But if Trump were to pursue diplomacy with Iran's leadership, he would have to overcome deep-seated concerns among Washington's closest regional allies, such as Saudi Arabia and Israel, who are deeply skeptical about negotiating with Rouhani's government.
"No preconditions. They want to meet, I'll meet, any time they want, any time they want".
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".
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He predicted DeSantis will win against Agriculture Commissioner Adam Putnam in the state's August 28 Republican primary. While the reasons for the early arrivals are plentiful, many said they're there to show support for the president.
Earlier Tuesday, a US official said Secretary of State Mike Pompeo had no intention of meeting his Iranian counterpart at an global gathering this weekend in Singapore. "There's nothing wrong with meeting", Trump said.
He continued, writing in all capital letters, that: "WE ARE NO LONGER A COUNTRY THAT WILL STAND FOR YOUR DEMENTED WORDS OF VIOLENCE & DEATH".
"I ended the Iran deal - it was a ridiculous deal".
Former US presidents learnt better than Trump that Iran and its people could not be threatened, and that they would instead close their ranks and strengthen their unity against any foreign threat and pressure, he added.
A return by the Trump administration to the deal, though, is considered highly unlikely.
The United States is going after Iran in a rather smart fashion despite the childish rhetoric being traded on social media.
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 tougher USA posture on Iran has fueled speculation that Trump is seeking to promote enough unrest to potentially unseat Iran's rulers. "I believe in meeting", Mr Trump said.
The three major European signatories to the 2015 deal have been searching for ways to salvage it but cautioned Tehran that they may not be able to persuade many major investors not to bolt from business with Iran to avoid US punishment.
"Respect for the great nation of Iran, the reduction of hostilities, and America's return to the JCPOA, will smooth the path past the current rocky relations", adviser Hamid Aboutalebi said.
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