Trump, attending the G7 with other leaders in France, also withdrew at least one of his stated rationales for attacking Iran in the first place, saying it would be "unfair" for Tehran not to have ballistic missiles, having previously vowed to obliterate them.
"We're going to bomb the hell out of them if they violate the agreement," Trump said of Iran at a press conference on Wednesday.
"I don't want them to. I want them to honour the agreement."
He also called Iranians "smart people" as US and Iranian negotiators work on a permanent truce over the coming 60 days.
Earlier, he had said: "If I don't like it, if they don't behave, we'll go right back to dropping bombs right smack in the middle of their head, OK?"
The memorandum includes an immediate end to the war on all fronts, including Lebanon, the full resumption of maritime traffic in the Strait of Hormuz, the lifting of a US blockade of Iranian ports, the waiving of international sanctions on Iran, the unfreezing of its assets, and a plan worth $US300 billion ($A426 billion) for the economic rehabilitation of the Islamic Republic.
Iran also undertakes not to build nuclear weapons, reaffirming a vow it had made for decades. Despite his typically combative rhetoric, Trump appears to have achieved little of what he said he wanted at the outset of the war, while Iran appears much closer to sanctions relief worth billions of dollars than before it was attacked.
Iran's theocratic government remains in place, its stockpile of highly enriched uranium has not been surrendered, its ballistic missile capabilities have not been destroyed and it has not ended its support for anti-Israel militias like Hezbollah in Lebanon.
Speaking to reporters in Paris, Trump recanted his promise in the war's early days to destroy all of Iran's missiles and "raze their missile industry to the ground".
"I'm saying that if other countries have them, it's a little bit unfair for them not to have some," Trump said after leaving the summit.
However, G7 leaders hailed the agreement at their summit, held in the French town of Evian-les-Bains, an hour's drive along the shore of Lake Geneva from where the US has said a formal signing ceremony for the US-Iran agreement was due to be held across the Swiss border on Friday.
But Iranian foreign ministry spokesperson Esmaeil Baghaei cast doubt on this, telling IRIB's News Network that, because the two presidents had already digitally signed the agreement, "No signing ceremony will be held in Switzerland."
European leaders also demanded an immediate ceasefire in Lebanon, where the memorandum calls for a halt to hostilities between Israel and the Iran-backed Hezbollah group that have displaced more than a million people.
Fighting there has abated but not ceased since the agreement was reached on Sunday, and Israel, which was not part of the negotiations and whose military is occupying southern Lebanon, says it retains the right to use force.
Trump on Wednesday gently rebuked Israeli Prime Minister Benjamin Netanyahu over his tactics in Lebanon against Hezbollah. The two men have repeatedly clashed over Israel's refusal to constrain its pursuit of Hezbollah in Lebanon, where a cessation of hostilities is a key Iranian demand.
"Netanyahu happens to be a good man, gets a little excited sometimes," Trump told reporters.
"We have a little dispute over Lebanon. I say you can do a little softer touch, Bibi," he said, using Netanyahu's nickname.
"You don't have to knock down a building every time somebody walks into it that's from Hezbollah."
Lebanese state media reported fresh Israeli air strikes and artillery fire in several southern towns throughout Wednesday. Lebanese security sources said Hezbollah had also launched two drone attacks on Israeli forces in the south. The group did not publicly claim the attacks.
Israel later said five of its soldiers had been injured in two Hezbollah drone attacks in southern Lebanon.
with DPA
