"I would certainly meet with Iran if they wanted to meet," Trump said on Monday during a joint news conference at the White House alongside Italian Prime Minister Giuseppe Conte.

"I do believe that they will probably end up wanting to meet. I'm ready to meet whenever they want to.

"No preconditions... They want to meet, I'll meet, whenever they want," the President added.

Trump also appeared to hedge the possibility of a meeting on an ability to "work something out that's meaningful".

Hamid Aboutalebi, an adviser to President Rouhani, tweeted in response to Trump that "returning to the nuclear deal" and "respecting the Iranian nation's rights" would pave way for talks, reports the BBC.

Such a meeting would be the first between US and Iranian leaders since the 1979 Iranian revolution.

Monday's olive branch from Trump marks an abrupt shift in tone. The President has been a strident critic of Iran, threatening Tehran with "consequences" on July 22, CNN reported.

The President and his senior officials have ramped up the rhetoric against Tehran, promising to "crush" its economy with international sanctions and accusing it of fomenting terrorism and regional instability, while telling the country's citizens that their leaders are corrupt.

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 Iran nuclear deal known as the Joint Comprehensive Plan of Action.

Iran insists its nuclear programme is entirely peaceful, and its compliance with the deal has been verified by the International Atomic Energy Agency (IAEA), which has said Iran is honouring its commitments.