He earlier told reporters the US has held talks with Iran and that the two sides had “major points of agreement”.
Trump said the conversations that took place on Sunday would continue on Monday and that if the negotiations continued productively, there would be a deal very soon.
Trump added that his Middle East envoy Steve Witkoff and son-in-law Jared Kushner held the talks.
“We have had very, very strong talks. We’ll see where they lead. We have major points of agreement, I would say, almost all points of agreement,” he said.
He did not name who in Iran the US had spoken to, but described him as “the man who I believe is the most respected and the leader.”
Trump said the US had not heard from Supreme Leader Mojtaba Khamenei. He said he did not know if Khamenei was alive, adding that he did not wish for him to be killed.
“They will never have a nuclear weapon,” Trump said, referring to Iran. “They’ve agreed to that.”
He said Iran had initiated contact because it did not want the US to strike its energy infrastructure, as Trump had threatened would happen unless the Strait of Hormuz was reopened.
“I think this is something that’s going to happen, and why wouldn’t it happen?” referring to a deal with Iran.
“So tomorrow morning, sometime their time, we were expected to blow up their largest electric generating plant that cost over $10 billion to build. It’s a very good one … Why would they want that? So they called, I didn’t call. They called,” he added.
“They want to make a deal, and we are very willing to make a deal,” he said, before adding, “We have a very serious chance of making a deal.”
Trump said the Strait of Hormuz would be open very soon “if this works”.
“The price of oil will drop like a rock as soon as the deal is done,” he said.
Trump earlier said he had given instructions to postpone any military strikes against Iranian power plants for five days, just hours ahead of a deadline that threatened further escalation in the conflict now in its fourth week.
Trump claimed in a post on his Truth Social platform that the US and Iran had had “VERY GOOD AND PRODUCTIVE” conversations over the past two days about a “COMPLETE AND TOTAL RESOLUTION OF HOSTILITIES IN THE MIDDLE EAST”.
The White House did not respond to questions about the content of the talks, who participated or where they were held.
Meanwhile, Iranian media reported that there were no negotiations between Tehran and Washington.
“There are no talks between Tehran and Washington,” said the Mehr news agency, citing Iran’s foreign ministry, adding that Trump’s statements were part of a push to reduce energy prices.
In his message, written entirely in capital letters, Trump said he had instructed the defence department to postpone the strikes pending the outcome of the talks.
He claimed while speaking to Fox Business Network that Iran wanted “badly to make a deal”, which could come within five days.
A source briefed on Israel’s war plans said Washington had kept it informed of its talks with Tehran, and that Israel was likely to follow Washington in suspending any targeting of Iranian power plants and energy infrastructure.
The Israeli prime minister’s office did not immediately respond to a request for comment on reported talks with Iran or Washington’s decision to suspend strikes on some Iranian targets.
Trump’s comments briefly sent the price of the Brent crude oil benchmark down around 13 per cent to back below $100 a barrel.
By 1245 GMT, it stood around $101.80.
Global markets also recovered sharply, with US stock futures reversing losses to gain around 1.3pc.
On Saturday, Trump had warned that Iranian power plants would be destroyed if Tehran failed to “fully open” the Strait of Hormuz to all shipping within 48 hours. Trump set a deadline of around 7:44pm EDT (2344 GMT) on Monday.
Iran’s Revolutionary Guards on Monday threatened retaliation, saying they would attack Israel’s power plants and those supplying US bases across the Gulf region if Trump followed through with his threat.
More than 2,000 people have been killed in the war that the US and Israel launched on February 28, which has upended markets, driven up fuel costs, accelerated global inflation fears and convulsed the Western defence alliance.
However, the threat of strikes on Gulf electricity grids raised fears of mass disruption to desalination for drinking water, and further rattled oil markets.
While attacks on electricity could hurt Iran, they could be catastrophic for its Gulf neighbours, which consume around five times as much power per capita.
Electricity makes their gleaming desert cities habitable, in part by powering the desalination plants that produce 100pc of the water consumed in Bahrain and Qatar. Such plants use seawater to meet more than 80pc of drinking water needs in the United Arab Emirates, and 50pc of the water supply in Saudi Arabia.
Tehran threatens to mine Gulf
Fatih Birol, executive director of the International Energy Agency, said the resulting energy crisis was worse than the two oil shocks of the 1970s and the gas shortage connected to Russia’s 2022 invasion of Ukraine put together.
Iran’s Defence Council escalated its threatened retaliation on Monday, prior to Trump’s delay, saying Tehran would cut all Gulf routes by laying sea mines if Trump followed through, state media reported.
“In this case, the entire Gulf will practically be in a situation similar to the Strait of Hormuz for a long time ” The Israeli military said early on Monday it had begun its latest broad wave of strikes on infrastructure in Tehran.
Iranian news agencies said six people had been killed and 43 injured in strikes on residential buildings in the western city of Khorramabad.
A strike on the southern city of Bushehr targeted the local meteorological organisation and killed the head of meteorology for Bushehr’s airport, state media reported.
The Iranian Red Crescent posted a video of a residential building in affluent northern Tehran with most of its facade destroyed and emergency staff rescuing someone on a stretcher from the upper floors.
Across the Gulf, the Saudi defence ministry said two ballistic missiles had been launched towards Riyadh. One was intercepted while the other fell in an uninhabited area.
Iran’s semi-official Fars News Agency reported Monday, citing what it described as informed Iranian sources, that plans are being prepared for potential actions targeting Tel Aviv and some regional allies of the United States and Israel.
“Special plans are arranged tonight for Tel Aviv and some regional allies of the US and Israel, which will completely remove any hope of negotiation from the minds of the aggressors,” a source was quoted as saying by Fars, which is affiliated with the Islamic Revolutionary Guard Corps.
The report did not provide further details about the nature of the alleged plans.
According to the same report, Iranian sources also suggested that the situation in the Strait of Hormuz may not return to its pre-war status even if the conflict eventually ends.
The Strait of Hormuz, located between Iran and Oman, is one of the world’s most critical maritime chokepoints, through which roughly 20% of global petroleum liquids consumption passes, making stability in the waterway vital for global energy markets.
(With additional input from News Desk)