Trump's remarks on social media concluded a day in which he 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 last month, 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.
The United States and Israel suspended their bombing campaign against Iran four weeks ago, but appear no closer to a deal to end a war that has caused the biggest disruption ever to global energy supplies, roiled global markets and raised worries about the possibility of a wider global economic downturn.
In his 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 that 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."
Iran's proposal to delay talks on nuclear issues until later appears to contradict Washington's repeated demand that Iran give up its stockpile of more than 400 kg of highly enriched uranium as a condition to end the war.
Washington says the uranium could be used to make a bomb. Iran says its nuclear program is peaceful but it is willing to discuss curbs on it in return for the lifting of sanctions, as it accepted in a 2015 deal that Trump abandoned.
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.
While saying repeatedly he is in no hurry, Trump is under domestic pressure to break Iran's hold on the strait, which has choked off 20 per cent of the world's oil and gas supplies and pushed up US petrol prices.
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.
