Trump, in a post on his Truth Social site, gave few details about the operation, including whether the US navy would be involved.
He described the effort, to begin on Monday in the Middle East, as a "humanitarian gesture" meant only to aid neutral countries that were not involved in the US-Israeli war on Iran.
"For the good of Iran, the Middle East, and the United States, we have told these Countries that we will guide their Ships safely out of these restricted Waterways, so that they can freely and ably get on with their business," Trump wrote in the post.
"Project Freedom" would begin on Monday morning, Trump said, and added that his representatives are having discussions with Iran that could lead to something "very positive for all".
Earlier, Trump said on social media he had yet to review the exact wording of a new Iranian peace proposal but he was unlikely to accept it, because the Iranians had not yet "paid a big enough price".
He also publicly mused about the possibility of restarting air strikes, the latest mixed signal as he seeks to end the war he launched more than two months ago.
On Sunday, Israel ordered thousands of Lebanese to leave villages in southern Lebanon, an escalation of a war between Israel and Iran's Hezbollah allies that has run in parallel to the Iran war and could further complicate wider peace efforts.
Iran has said talks with Washington cannot resume unless a ceasefire also holds in Lebanon, which Israel invaded in March to attack Hezbollah after the Iranian-backed Lebanese group fired across the border in support of Tehran.
Lebanon and Israel agreed a separate truce in March, but fighting has continued, though on a smaller scale.
The Israeli military issued an urgent warning on Sunday to residents of 11 towns and villages in Lebanon's south, urging them to evacuate their homes and move at least 1000 metres away to open areas.
The military said it was conducting operations against Hezbollah following what it described as a violation of the ceasefire, warning that anyone near Hezbollah fighters or facilities could be at risk.
In a post on social media, Trump wrote: "I will soon be reviewing the plan that Iran has just sent to us, but can't imagine that it would be acceptable in that they have not yet paid a big enough price for what they have done to Humanity, and the World, over the last 47 years."
On Saturday, a senior Iranian official had said Iran's proposal would first open shipping in the Strait of Hormuz and end a US blockade of Iran, while leaving talks on Iran's nuclear program for later.
Though Trump had already said on Friday he was not satisfied with the Iranian proposal, he said on Saturday he had yet to hear all the details.
"They told me about the concept of the deal. They're going to give me the exact wording now," he said.
Asked if he might restart strikes on Iran, Trump replied: "I don't want to say that. I mean, I can't tell that to a reporter. If they misbehave, if they do something bad, right now we'll see. But it's a possibility that could happen."
Reuters and other news organisations have reported over the past week that Tehran was proposing to reopen the strait before nuclear issues were resolved. The senior Iranian official confirmed that this new timeline had now been spelled out in a formal proposal conveyed to the United States through mediators.
Iranian media said Tehran's 14-point proposal included the withdrawal of US forces from areas surrounding Iran, lifting the blockade, releasing Iran's frozen assets, payment of compensation, lifting sanctions and ending the war on all fronts, including Lebanon, as well as a new control mechanism for the strait.
With AP
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