The reopening of one of the world's most important energy chokepoints would mark a major step toward ending months of deadly conflict and economic turmoil triggered by US-Israeli strikes on Iran in late February.

"Ships are starting to move, many loaded up with Oil, out of the Strait of Hormuz," Trump said, adding later that he did not "think we will need much help" keeping the waterway open.

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Iranian media reported on Monday evening that three oil tankers and two cargo ships carrying goods had passed through the area that had been subject to a US naval blockade.

Iran had blockaded the strait since the start of the war, sending oil prices soaring and raising fears of a prolonged inflation shock. The United States then blocked shipping to and from Iranian ports.

The US, Iran and mediator Pakistan said the peace agreement was to be signed Friday in Switzerland.

A senior US administration official, however, said Trump, Vice President JD Vance and Iran's parliamentary speaker Mohammad Bagher Ghalibaf had already signed the text electronically.

"The president wanted to sign it personally because he wanted to show his... dedication to bring this through to a successful resolution," said the official.

Asked at the G7 in France when the text would be released, Trump said: "It's a very powerful document, and I want it to be released. So probably pretty soon."

Iran's Deputy Foreign Minister Kazem Gharibabadi said the deal brought an "immediate end" to the war, with talks on a "final agreement" to be held within two months.

His country's military hailed the accord as a victory, claiming it had "humiliated" the US and Israel, while President Masoud Pezeshkian called it "a great achievement" for the region.

But Iranian Foreign Minister Abbas Araghchi struck a more cautious note.

"We have a history of broken commitments," he said. "We have a history of agreements being torn up. All of this is present in our minds."

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Iran's foreign ministry spokesman Esmaeil Baqaei said Washington must ensure that Israel stops fighting in Lebanon under the agreement.

Lebanon was pulled into the war in early March when Iran-backed Hezbollah launched rockets at Israel after the killing of Iran's supreme leader, prompting Israeli strikes and a ground invasion.

"The United States must honour its commitments. It must ensure that the Zionist regime also respects its own regarding Lebanon," Baqaei said.

But Israeli Prime Minister Benjamin Netanyahu said the country's forces would remain in Lebanon, Syria and Gaza "as long as necessary".

He said the war with Iran had spared Israel from the Islamic republic's threat of "nuclear annihilation", while Israeli figures across the political spectrum criticized the deal.

Lebanese President Joseph Aoun welcomed the agreement during a call with Araghchi, saying he hoped it would be a "positive step towards reducing tensions".

Lebanese state media later reported the first deadly strike since the announcement, saying the Israeli attack in the south killed one person.

Hezbollah, which thanked Iran for insisting Lebanon be included in the deal, said it had repelled an Israeli force trying to "advance" in southern Lebanon.

The deal follows weeks of fraught negotiations and threats of renewed hostilities, but key details remain unclear.

Baqaei said Washington had "committed" to releasing frozen Iranian funds abroad and compensating Tehran for wartime damage.

Iran's Mehr news agency had reported the US would release $12 billion in frozen assets before negotiations begin.

Baqaei said Tehran would seek UN Security Council ratification after negotiating a final agreement on its nuclear programme.

That could prove contentious as Washington presses to end Iran's nuclear ambitions and address its stockpile of highly enriched uranium, said to have been buried by US strikes last year.

Trump told The New York Times the US was still negotiating whether Iran would suspend enrichment for 20 years, hinting he might settle for 15.

Baqaei said Iran would charge maritime service fees, rather than tolls, on shipping through Hormuz.

The announcement of the agreement sent oil prices sharply lower and lifted global stocks, with traders betting that the reopening of a route that normally carries about 20 percent of the world's crude would ease pressure on energy supplies.

Crude prices fell nearly five percent toward $80 a barrel after having surged above $110 soon after the war began, while the Dow hit a fresh record and the Nasdaq jumped more than three percent.

In Tehran, English teacher Arya, 38, said "our people will not return to normal".

"They came to understand that Trump is not their ally," he said.

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