Mr Trump recently warned the Iranian President to "be cautious" in an all-caps Twitter post. (Image: PA)
US President Donald Trump has said that he would meet with Iranian President Hassan Rouhani without preconditions.
Speaking during a joint news conference with Italy's premier Giuseppe Conte, Mr Trump said he would meet with the Iranians "anytime they want to".
"I'll meet with anybody. There's nothing wrong with meeting."
The overture comes as Mr Trump and the Iranians have been escalating their rhetoric after Mr Trump's May withdrawal from the landmark nuclear accord.
The United States has also vowed to boost sanctions until Iran changes its regional policies, including its support for regional militant groups.
It is unclear whether Mr Rouhani has any interest in meeting with Mr Trump.
Mr Rouhani's chief of staff claimed earlier this month in Iran's state-owned newspaper that Mr Rouhani had rejected eight requests from Mr Trump for one-on-one talks last year.
Rouhani recently warned the US that "war with Iran is the mother of all wars", prompting an all-caps retort from Mr Trump last week:
Iranian foreign minister Mohammad Javad Zarif fired back with his own message that began, "COLOUR US UNIMPRESSED."
Mr Trump tempered his threatening rhetoric two days later when he said his administration stands ready for Iran to come back to the negotiating table, saying:
"We're ready to make a real deal, not the deal that was done by the previous administration, which was a disaster."
Mr Trump paints himself as a master negotiator who is most effective when he meets with his counterparts face-to-face. He pointed to his recent one-on-ones with North Korea's Kim Jong Un and Russia's Vladimir Putin as examples of the benefits of such get-togethers.
"I believe in meeting," he said, talking up the benefits of "speaking to other people, especially when you're talking about potentials of war and death and famine and lots of other things".
Asked whether he would set any preconditions for the meetings, Mr Trump was clear.
"No preconditions, no. If they want to meet, I'll meet anytime they want, anytime they want.
"Good for the country, good for them, good for us and good for the world. No preconditions. If they want to meet, I'll meet."
US secretary of state Mike Pompeo told reporters he was on board with the president's invitation, saying Mr Trump "wants to meet with folks to solve problems".
But he appeared to add several qualifications: "If the Iranians demonstrate a commitment to make fundamental changes in how they treat their own people, reduce their maligned behaviour, can agree that it's worthwhile to enter in a nuclear agreement that actually prevents proliferation, then the president said he's prepared to sit down and have a conversation with him."