"I'd meet with anybody. I believe in meetings," the US president told reporters at the White House.
Mr Trump's conciliatory approach comes after he and Iranian President Hassan Rouhani traded hostile warnings earlier this month.
In May, the US left a deal which curbed Iran's nuclear activities in return for the lifting of international sanctions.
Washington is preparing to re-impose sanctions on Tehran within days - despite objections from the UK, France, China, Russia and Germany, which also signed the 2015 agreement.
The US is deeply suspicious of Iranian activity in the Middle East and is an ally of Israel and Saudi Arabia, two of Iran's foes.
"If they want to meet, we'll meet," Mr Trump said.
Hamid Aboutalebi, an adviser to President Rouhani, tweeted in response to Mr Trump that "returning to the nuclear deal" and "respecting the Iranian nation's rights" would pave way for talks.
Such a meeting would be the first between US and Iranian leaders since before the 1979 Iranian revolution.
Mr Trump's abrupt change in tone also echoes the run-up to his meeting with North Korean leader Kim Jong-un, another diplomatic first, which took place after the two leaders had previously traded insults and threats.
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