Trump's conciliatory approach comes after he and Iranian President Hassan Rouhani traded hostile warnings earlier this month, leading Rouhani, to warn the US that war with Tehran would be the "mother of all wars."
US President Donald Trump has offered to meet Iran's leaders to discuss how to improve ties.
Relations have deteriorated since he pulled the United States out of the 2015 Iran nuclear deal, threatening to impose sanctions.
On Monday, speaking at a news conference with visiting Italian prime minister Giuseppe Conte, Trump said:
"I would certainly meet with Iran if they wanted to meet. I don't know that they're ready yet, they're having a hard time right now. But I ended the Iran deal. It was a ridiculous deal. I do believe that they will probably end up wanting to meet."
Trump said he had "no preconditions" for a meeting with the Iranians, adding: "If they want to meet, I'll meet."
Hours before Trump's statement, Tehran had ruled out talks with Washington.
Trump's conciliatory approach comes after he and Iranian President Hassan Rouhani traded hostile warnings earlier this month.
A week ago, Trump lashed out at Rouhani in a tweet, saying "Never, ever threaten the United States again or you will suffer consequences the likes of which few throughout history have ever suffered before."
Iran brushed off Trump’s threatening tweet with an all-caps message of its own.
Shortly before that July 22 tweet, Rouhani had addressed Trump in a speech, saying that hostile U.S. policies could lead to "the mother of all wars".
A tweet from a Tehran adviser suggests "returning to the deal" and "respecting Iranian rights" would pave the way for talks.
Washington is to re-impose sanctions on Tehran - despite objections from the UK, France, China, Russia and Germany, which also signed the 2015 agreement.