Washington (CNN) President Donald Trump said Monday he is willing to meet with Iran's leadership, without preconditions, "whenever they want," a sharp departure from his threats against the regime last week.

"I would certainly meet with Iran if they wanted to meet," Trump said 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," he added. "They want to meet, I'll meet, whenever they want."

Monday's olive branch from Trump marks an abrupt shift in tone, and may be little more than theater with US midterm elections looming on the horizon. The President has been a strident critic of Iran, threatening the regime with "consequences" as recently as July 22, while his administration pursues a strategy that many see as regime change in all but name.

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.

Iranian President Hassan Rouhani did not address Trump's comments on Tuesday, instead focusing on the "illegal" US withdrawal from the Iran nuclear deal back in May, in a statement posted on his official website.

"After the US's illegal withdrawal from the JCPOA (Joint Comprehensive Plan of Action), the ball is in Europe's court in the limited time remaining," said Rouhani of the deal, as part of a report about his meeting with British Ambassador to Tehran Rob Macaire.

The international nuclear agreement forced Iran to curtail its uranium enrichment capacity to prevent it from developing nuclear weapons, and imposed stringent verification processes, in exchange for relief on crippling sanctions.

The remaining members of the Iran nuclear deal are still committed to the international pact, as is Iran.

'Nothing wrong with meeting'

Trump touted the benefits of diplomacy, saying he would "meet with anybody" and once again argued that his July 12 meeting with Russian President Vladimir Putin -- which drew heated bipartisan criticism -- was a success.

"Speaking to other people, especially when you're talking about potentials of war and death and famine and lots of other things -- you meet. There's nothing wrong with meeting," Trump said.

While Trump said he would apply no preconditions to meeting with Iran, he did appear to hedge the possibility of a meeting on an ability to "work something out that's meaningful."

Secretary of State Mike Pompeo said the President had made the offer before. "The President wants to meet with folks to solve problems," Pompeo told CNBC. "If the Iranians demonstrate a commitment to make fundamental changes in how they treat their own people, reduce their malign behavior, can agree that it's worthwhile to enter into a nuclear agreement that actually prevents proliferation, then the president said he's prepared to sit down and have the conversation with them."

The President's sudden willingness to consider a meeting with Iran's leaders echoes his about-face on meeting with North Korean despot Kim Jong Un. Trump has suggested in the past that financial pressure would eventually bring Tehran to the table. Iran's leaders have shown little interest in engaging with the US, however, particularly given the Trump administration's decision to leave the nuclear accord and -- in an echo of its approach to North Korea -- its subsequent drive to squeeze Iran's economy.

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After leaving the deal, the Trump White House has moved to reinstate sanctions on Tehran in two major tranches. Some will be reimposed in August and target autos, gold and other key metals, while others will snap back in November and target the energy sector and transactions with Iran's central bank.

The sanctions would punish firms that do business with Iranian entities. Brian Hook, the State Department's director of policy planning, said on July 2 that more than 50 international firms have already announced their plans to leave Iran, "particularly in the energy and finance sectors."

Iranian President Hassan Rouhani did leave open the door to the possibility of engagement with the US this month in Tehran when he said that Americans "must understand that war with Iran is the mother of all wars and peace with Iran is the mother of all peace," according to the state-run news agency IRNA.

To Iranian President Rouhani: NEVER, EVER THREATEN THE UNITED STATES AGAIN OR YOU WILL SUFFER CONSEQUENCES THE LIKES OF WHICH FEW THROUGHOUT HISTORY HAVE EVER SUFFERED BEFORE. WE ARE NO LONGER A COUNTRY THAT WILL STAND FOR YOUR DEMENTED WORDS OF VIOLENCE & DEATH. BE CAUTIOUS! — Donald J. Trump (@realDonaldTrump) July 23, 2018

But talks seem highly unlikely anytime soon. In his July 22 tweet, Trump said, "To Iranian President Rouhani: NEVER, EVER THREATEN THE UNITED STATES AGAIN OR YOU WILL SUFFER CONSEQUENCES THE LIKES OF WHICH FEW THROUGHOUT HISTORY HAVE EVER SUFFERED BEFORE."

He continued, writing in all capital letters, that: "WE ARE NO LONGER A COUNTRY THAT WILL STAND FOR YOUR DEMENTED WORDS OF VIOLENCE & DEATH. BE CAUTIOUS!"

Senior administration officials have also deployed increasingly aggressive rhetoric on Iran. The day before Trump's fiery tweet, Pompeo likened the Iranian regime to the mafia and accused the ruling clerics of enriching themselves and funding terrorism at the expense of ordinary Iranians in a speech at the Ronald Reagan National Library in Simi Valley, California.

"To the regime, prosperity, security and freedom for the Iranian people are acceptable casualties in the march to fulfill the revolution," Pompeo said. "The level of corruption and wealth among regime leaders shows that Iran is run by something that resembles the mafia more than a government."