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Trump's surprise announcement to reporters in Florida was short on detail about whom the US side had contacted, but he said it was "not the supreme leader", Mojtaba Khamenei.
He described the unidentified negotiator as "a top person" and a "most respected" leader. Trump said there were already "major points of agreement" with the Iranian negotiators. US conditions, he added, included Iran abandoning any nuclear ambitions and giving up its enriched uranium stockpiles.
Trump said the unidentified Iranian officials reached out under pressure of his threat to attack power stations.
"They called, I didn't call," he said. "They want to make a deal, and we are very willing to make a deal."
"We're going to get together today, by probably phone, because it's very hard to find a country – it's very hard for them to get out, I guess," Trump told reporters before boarding his plane.
Watch moreTrump threat to hit Iran power plants could violate Geneva Conventions
Trump was speaking shortly after he backed down from a threat to bombard Iran's power stations at the expiration of a late-Monday deadline – an escalation Iran vowed would be met by reprisals on Gulf infrastructure targets and desalination plants, further roiling the US and world economies.
Trump over the weekend warned the US would “obliterate” Iran’s power plants if it doesn’t fully open the Strait of Hormuz within 48 hours.
Trump announced Monday on his Truth Social site that he was allowing five days for talks, citing "very good and productive" talks with Iran over the past two days.
Asked why he wouldn't identify the people talking to the United States, Trump said "because I don't want them to be killed".
But if talks don't produce results, he told reporters later, "we'll just keep bombing our little hearts out".
Read moreIran threatens to ‘completely close’ Hormuz Strait, Israel strikes Lebanon bridges
Tehran denies negotiating
Iranian sources said no talks were under way, with Iran’s parliament speaker denying there had been any recent negotiations with the United States.
“No negotiations have been held with the US, and fakenews is used to manipulate the financial and oil markets and escape the quagmire in which the US and Israel are trapped,” Speaker Mohammad Bagher Qalibaf wrote on X.
"There are no talks between Tehran and Washington," the Mehr news agency reported, citing Iran's foreign ministry, adding that Trump's statements were part of a push "to reduce energy prices".
Trump's backtrack on attacking Iranian energy sites came just hours before Wall Street was set to open after brutal selloffs on European and Asian markets and a further climb in the price of oil.
The oil price has posed an increasing political headache for Trump as Americans complain of higher prices at the pump, ahead of crucial midterm elections in November that will determine the make-up of Congress.
Shortly after Trump’s announcement – hours before the deadline was set to expire – Iranian state television declared that the American leader had backed down “following Iran’s firm warning”.
Iran has lost a swath of leadership to US and Israeli bombing. Mojtaba Khamenei is the son of the previous supreme leader, but he has not been seen in public since the war began and US officials say he may be badly injured.
Trump has said he does not know whom to negotiate with because so many leaders have been killed.
On Monday he dismissed Khamenei, saying, "I don't consider him really the leader."
(FRANCE 24 with AFP and AP)