Trump said the US is negotiating with Iran's parliamentary speaker, Mohammad Bagher Ghalibaf, in an interview with the New York Post.
The former Revolutionary Guard commander was previously floated as Washington's negotiating partner, denied Iran is talking to the US and said Pakistan-facilitated discussions were merely a cover for American troop deployments.
The comments came after after Tehran earlier described US peace proposals as "unrealistic" and fired waves of missiles at Israel.
Israel's military said two drones from Yemen had also been intercepted on Monday, two days after the Iran-aligned Houthis entered the war by firing missiles at Israel, and that Lebanon's Hezbollah had fired rockets at Israel.
Israeli forces carried out missile strikes on what they called military infrastructure in Tehran and infrastructure used by Iran-aligned Hezbollah in Beirut, leaving black smoke hanging over the Lebanese capital.
Turkey's defence ministry said a ballistic missile launched from Iran entered Turkish airspace before being shot down by NATO air and missile defences deployed in the eastern Mediterranean.
Iran remained defiant in the month-old war, which began with US-Israeli attacks on Iran on February 28 and has spread across the region, killing thousands, disrupting energy supplies and hitting the global economy.
Iran has largely blocked the Strait of Hormuz, a narrow waterway which normally carries about a fifth of global oil and liquefied natural gas supplies.
Iran said on Monday it had received US peace proposals via intermediaries, following talks on Sunday between the foreign ministers of Pakistan, Egypt, Saudi Arabia and Turkey.
But Iranian Foreign Ministry spokesman Esmaeil Baghaei said the proposals were "unrealistic, illogical and excessive".
"Our position is clear. We are under military aggression. Therefore, all our efforts and strength are focused on defending ourselves," he told a press conference.
Soon after Baghaei's remarks, Trump said in a social media post that the United States was in talks with a "more reasonable regime" to end the war in Iran but he also issued a new warning over the Strait of Hormuz.
"Great progress has been made but, if for any reason a deal is not shortly reached, which it probably will be, and if the Hormuz Strait is not immediately 'Open for Business,' we will conclude our lovely 'stay' in Iran by blowing up and completely obliterating all of their Electric Generating Plants, Oil Wells and Kharg Island," Trump wrote.
Trump also threatened a US attack on the desalination plants that supply clean water in Iran.
He said last week he would pause attacks on Iran's energy plants for 10 days, which would be until April 6, US time.
A Pakistani security official, whose country is trying to mediate in the war, said at this stage it appeared unlikely there would be direct US-Iran talks this week.
Baghaei also said Iran's parliament was reviewing a possible exit from the Nuclear Non-Proliferation Treaty, which recognises the right to develop, research, produce and use nuclear energy as long as nuclear weapons are not pursued.
Trump has cited preventing Iran obtaining nuclear weapons as one of the reasons for attacking Iran on February 28. Iran denies it is seeking a nuclear arsenal.
Israeli Prime Minister Benjamin Netanyahu, in an interview with US media outlet Newsmax, declined to give a timeline for achieving his country's objectives in the war.
While he said that "it's definitely beyond the halfway point," he later clarified that he meant in terms of missions, not time.
The White House said Trump was considering asking Arab nations to pay for the cost of the war.
"It's an idea that I know that he has and something that I think you'll hear more from him on," Leavitt said in response to a reporter's question about the idea.
His administration requested an additional $US200 billion in funding for the war, which faces stiff opposition in the US Congress, which must approve new spending.
with AP and DPA
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