US President Donald Trump said Monday that he would meet with Iran's leadership without preconditions, only to be contradicted by the White House and his top diplomat hours later.

"I would certainly meet with Iran if they wanted to meet. I don't know that they are ready yet. They are having a hard time right now," Trump said during a news conference with Italy's prime minister. "I'll meet with anybody," Trump said. "There's nothing wrong with meeting."

"I do believe they will probably end up wanting to meet. I'm ready to meet anytime they want to," he said, adding that he would do so without preconditions.

"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," Trump said.

Read more: Iran's currency drops 14 percent in one day on sanctions fears

Sanctions after withdrawl

The comments came as Washington prepares to impose what it describes as crushing sanctions on Tehran following Trump's decision earlier this year to unilaterally withdrawal the United States from the 2015 nuclear deal between Iran and six major powers. The deal was made in response to fears that Iran was developing an atomic bomb.

The first sanctions go back into effect in August, followed by ones on Iran's energy sector in November.

Trump's decision has created a growing gap between the United States and its European allies who are now trying to save the nuclear deal that the UN and non-proliferation experts say is robust and working.

Read more: US rejects EU request for Iran sanctions relief

White House, Pompeo backtrack 

Hours after Trump's comments, Secretary of State Mike Pompeo appeared to contradict his boss' statements about meeting with Iranian President Hassan Rouhani without preconditions.

"If the Iranians demonstrate a commitment to make fundamental changes in how they treat their own people, reduce their maligned behavior, 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," Pompeo said on CNBC.

In May, Pompeo unveiled the United States' Iran strategy, saying that Washington would not try to renegotiate the nuclear accord. Instead, any new deal would require Iran to meet 12 demands, including halting its ballistic missile program and ending its regional role in conflicts in the Middle East, including in Syria and Yemen.

Analysts say the United States is trying to instigate internal upheaval in Iran with a goal of regime change.

Read more: Pompeo unveils US Iran plan: Economic strife, break with EU  

White House National Security Council spokesman Garrett Marquis said Trump was open to dialogue and lifting sanctions only "if there are tangible, demonstrated and sustained shifts in Tehran's policies."

"Until then, the sting of sanctions will only grow more painful if the regime does not change course," he said.

Iran responds

In response to Trump's overture, Iran said the United States should return to the nuclear deal it exited in May if it wants to talk.

"Respecting the Iranian nation's rights, reducing hostilities and returning to the nuclear deal are steps that can be taken to pave the bumpy road of talks between Iran and America," Hamid Aboutalebi, an adviser to Rouhani, tweeted on Tuesday.

Iran-US war of words

The conflicting messages from the Trump administration come as Iran and the United States have ratcheted up a bitter war of word in recent weeks amid heightened tensions in the Middle East.

Rouhani last week warned the United States that Trump should "not play with the lion's tail."

"America should know that peace with Iran is the mother of all peace, and war with Iran is the mother of all wars," Rouhani said.

Trump responded with threats via Twitter.

"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!" he wrote.

In response to Trump's Twitter threats, Iranian Foreign Minister Mohammad Javad Zarif fired back with his own Twitter message that began, "COLOR US UNIMPRESSED."

The powerful head of Quds Force of the Islamic Revolutionary Guard Corps also issued a stern warning.

Read more: Iran's military power: What you need to know

"We are near you, where you can't even imagine. We are the nation of martyrdom," said Major General Qassem Soleimani. "You are aware of our power in the region and capability for [launching] asymmetrical war?"

Art of the deal?

Trump has portrayed himself as a master dealmaker who can hold one-on-one meetings with the United States' rivals and enemies, highlighted by recent talks with Russian President Vladimir Putin and North Korean strongman Kim Jong Un.