Trump said the vital waterway would be "completely open" from Friday, adding that he did not "think we will need much help" on keeping it open.

"Ships are starting to move, many loaded up with Oil, out of the Strait of Hormuz," the US leader said earlier.

Iran had blockaded the strait since the start of the war, which began with US-Israeli strikes on the Islamic republic in late February.

News of the deal sparked relief after months of deadly violence and global economic chaos.

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

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

"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 when the text of the agreement will be released, Trump said at the G7 in France: "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 put an "immediate end" to the war and that they would hold talks to seek a "final agreement" within two months.

Iran's military hailed the agreement as a victory, claiming it had "humiliated" the US and Israel, while President Masoud Pezeshkian said the deal was "a great achievement" for the region.

But Iranian Foreign Minister Abbas Araghchi spoke of "mistrust".

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

- Lebanon -

Iran's foreign ministry spokesman Esmaeil Baqaei said the US must ensure that Israel commits to stopping the war in Lebanon under the deal.

Lebanon was pulled into the Middle East war in early March when Iran-backed militant group Hezbollah launched rocket attacks on Israel in retaliation for 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.

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

He said the war with Iran had spared Israel from what he described as the Islamic republic's threat of "nuclear annihilation".

Israeli figures across the political spectrum had slammed the deal.

Lebanese President Joseph Aoun welcomed the agreement during a call with Araghchi.

Aoun said he hoped the deal would be a "positive step towards reducing tensions", while Araghchi emphasised "the importance of respecting Lebanon's sovereignty".

Lebanese state media reported the first deadly strike since the deal's 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 that was trying to "advance" in southern Lebanon.

- Terms unclear -

The deal follows weeks of fraught negotiations and periodic threats of fresh hostilities, but its details remain unclear.

Baqaei said Washington had "committed" to releasing Iran's frozen funds abroad and compensating it for damages during the war.

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

Baqaei said Tehran would seek ratification from the UN Security Council after it negotiates a final agreement covering its nuclear programme.

The details may prove contentious as the US presses its effort to end Tehran's nuclear ambitions and deal with 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 its enrichment for 20 years.

He hinted that he might settle for a 15-year suspension.

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

Iraq welcomed the strait's planned reopening.

UN Secretary-General Antonio Guterres called the deal a "critical step" towards resolving the war.

Saudi Arabia and Egypt welcomed the agreement, while Pakistan called it a "historic step towards peace".

The United Kingdom, France, Germany and Italy said they were prepared to lift sanctions imposed on Iran.

The announcement brought relief at market opening on Monday, with the Dow rising to a new intraday record after oil prices were already dropping sharply lower.

But 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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THE NEW YORK TIMES COMPANY