Trump scolded both sides for early violations of the truce he announced, but directed especially stinging criticism at Washington's close ally Israel over the scale of its strikes, telling it to "calm down now".
He later said Israel called off further attacks at his command to preserve the deal to end a 12-day air war with Iran.
Both Iran and Israel sent signals the conflict was over, at least for now.
President Masoud Pezeshkian hailed a "great victory" in a war he said Iran had successful ended, according to Iranian media.
Iran's official news agency IRNA earlier reported Pezeshkian as saying during a phone call with Saudi Crown Prince Mohammed bin Salman that Iran was ready to resolve differences with the US based on international frameworks.
Israel's military, meanwhile, said all regions of the country had moved to full activity level without restrictions from 8pm (local time). Its airport authority said Ben Gurion Airport had reopened.
Israeli armed forces chief of staff Eyal Zamir said the military was at "the conclusion of a significant chapter but the campaign against Iran is not over", though he added the military was refocusing on its war against Hamas in Gaza.
Whether the Israel-Iran truce can hold is a major question. Signaling a difficult path ahead, it took hours for Israel and Iran to even acknowledge that they had accepted the ceasefire that Trump said he had brokered.
Still, oil prices plunged and stock markets rallied worldwide in a sign of confidence arising from the ceasefire pact,which was taken to mean there would be no threat of disruption to critical oil supplies from the Gulf.
CEASEFIRE VIOLATIONS?
Iran and Israel earlier on Tuesday accused each other of violating the truce.
Trump, en route to a NATO summit in Europe, admonished Israel with an obscenity in an extraordinary outburst at an ally whose air war he had joined two days before by dropping massive bunker-buster bombs on Iran's underground nuclear sites.
"All planes will turn around and head home, while doing a friendly 'Plane Wave' to Iran. Nobody will be hurt, the Ceasefire is in effect!" Trump said in a post on Truth Social.
That followed a post in which he had said: "Israel. Do not drop those bombs. If you do it it is a major violation. Bring your pilots home, now!"
Before departing the White House, Trump told reporters he was unhappy with both sides for breaching the ceasefire, but particularly frustrated with Israel, which he said had "unloaded" shortly after agreeing to the deal.
"I've got to get Israel to calm down now," Trump said. Iran and Israel had been fighting "so long and so hard that they don't know what the f*** they're doing."
Prime Minister Benjamin Netanyahu's office acknowledged that Israel had bombed a radar site near Tehran in what it said was retaliation for Iranian missiles fired three-and-a-half hours after the ceasefire had been due to begin.
It said Israel had decided to refrain from further attacks following a call between Netanyahu and Trump, but did not explicitly say whether the strike on the radar site took place before or after they spoke.
The Islamic Republic denied launching any missiles and said Israel's attacks had continued for an hour-and-a-half beyond the time the truce was meant to start.
Pezeshkian said later Tehran would not violate the ceasefire unless Israel did so, and that it was prepared to return to the negotiating table, without elaborating, according to state-run Nournews.
A SENSE OF RELIEF
In both countries there was a palpable sense of relief that a path out of war had been charted, 12 days after Israel launched it with a surprise attack, and two days after Trump joined in with strikes on Iranian nuclear targets.
"We're happy, very happy. Who mediated or how it happened doesn't matter. The war is over. It never should have started in the first place," said Reza Sharifi, 38, heading back to Tehran from Rasht on the Caspian Sea, where he had relocated with his family to escape the airstrikes.
Arik Daimant, a software engineer in Tel Aviv, said: "Regrettably, it's a bit too late for me and my family, because our house back here was totally destroyed in the recent bombings last Sunday. But as they say: 'better late than never', and I hope this ceasefire is a new beginning."
Speaking to reporters on board Air Force One heading to the NATO summit, Trump said he did not want to see Iran's ruling system toppled.
"I don't want it. I'd like to see everything calm down as quickly as possible. Regime change takes chaos and ideally we don't want to see so much chaos," he said.
"Iran's not going to have a nuclear weapon, by the way, I think it's the last thing on their mind right now."
In the hours before the truce took effect, four people - one of them an off-duty Israeli soldier - were killed by Iranian missiles that hit a residential building in Beersheba in southern Israel, according to the Israeli ambulance service.
Iranian officials said nine people were killed by a strike on a residential building in northern Iran.
NUCLEAR TARGETS
Israel launched the surprise air war on June 13, hitting Iranian nuclear sites where it said Iran was trying to develop an atomic bomb and killing top military commanders in the worst blow to the Islamic Republic since the 1980s war with Iraq.
Iran says its uranium enrichment programme is for peaceful purposes and denies trying to build nuclear weapons.
Iranian authorities said hundreds of people were killed in Israel's airstrikes. Full information about the extent of the damage to nuclear and economic infrastructure could not be confirmed independently, with media tightly controlled in Iran.
Retaliatory missile strikes have killed 28 people in Israel, the first time large numbers of Iranian missiles have penetrated its air defences.
A senior White House official said Trump brokered the ceasefire deal with Netanyahu, and other administration officials were in touch with the Iranians. Qatar's Prime Minister Sheikh Mohammed bin Abdulrahman Al Thani secured Tehran's agreement during a call with Iranian officials, an official briefed on the negotiations told Reuters on Tuesday.
