The announcement added to optimism that the Iran war could be nearing an end, the Reuters news agency reported.
Trump said Iran wanted to make a deal and had offered to forgo nuclear weapons for more than 20 years.
"We’re going to see what happens, but I think we’re very close to making a deal with Iran," he told reporters outside the White House.
"I think we have a chance. And if that happens, oil goes way down, prices go way down, inflation goes way down—and ... much more importantly ... you won’t have a nuclear holocaust," he added.
Tehran’s nuclear ambitions were a sticking point at talks in Pakistan's capital Islamabad last weekend, according to earlier reports.
"We have a very good relationship with Iran right now, as hard as it is to believe. And I think it’s a combination of about four weeks of bombing and a very powerful blockade," Trump said.
At last weekend's talks in Islamabad, the United States proposed a 20-year suspension of all nuclear activity by Iran, while Tehran suggested a halt of three to five years, Reuters reported, citing people familiar with the proposals.
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Source: Reuters, IAR, PAP