Trump, speaking in The Hague where he attended a NATO summit on Wednesday, said his decision to join Israel's attacks by targeting Iranian nuclear sites with huge bunker-busting bombs had ended the war, calling it "a victory for everybody".
He shrugged off an initial assessment by the US Defense Intelligence Agency that Iran's path to building a nuclear weapon might have been set back only by months, saying the findings were "inconclusive" and he believed the sites had been destroyed.
"It was very severe. It was obliteration," he said.
He was confident Tehran would not try to rebuild its nuclear sites and would instead pursue a diplomatic path towards reconciliation, he said.
If Iran tried to rebuild its nuclear program, "We won't let that happen. Number one, militarily we won't," he said, adding: "I think we'll end up having something of a relationship with Iran to see (to) it."
Israel's bombing campaign, launched with a surprise attack on June 13, wiped out the top echelon of Iran's military leadership, killed its leading nuclear scientists and targeted nuclear sites and missiles.
Iran responded with missiles that pierced Israel's defences in large numbers for the first time.
Iranian authorities said 610 people were killed and nearly 5000 injured in Iran, where the extent of the damage could not be independently confirmed because of tight restrictions on media, while 28 people were killed in Israel.
A rapprochement between Tehran and the West would still require a deal governing Iran's long-term nuclear ambitions in return for lifting US and international sanctions.
The head of the UN's IAEA nuclear watchdog, Rafael Grossi, said his top priority was ensuring international inspectors could return to Iran's nuclear sites.
Iran had notified the watchdog during the war that it was taking special measures to protect nuclear material, but in order to verify what had happened to it, inspections must resume, he said.
Trump's Middle East envoy, Steve Witkoff, said late on Tuesday that talks between the United States and Iran were "promising" and Washington was hopeful for "a long-term peace agreement that resurrects Iran".
Iran's parliament approved a bill on Wednesday to suspend co-operation with the IAEA, but such a move would require approval of Iran's top security body.
Hours after Trump announced the ceasefire, he claimed credit for preserving it by ordering Israel to halt further attacks with its planes already in flight.
He used an obscenity on live television to say the enemies had been fighting so long they did not know what they were doing.
Both Iran and Israel declared victory: Israel claiming to have achieved its goals of destroying Iran's nuclear sites and missiles, and Iran claiming to have forced the end of the war by penetrating Israeli defences with its retaliation.
"We have removed two immediate existential threats to us: the threat of nuclear annihilation and the threat of annihilation by 20,000 ballistic missiles," Israel's Prime Minister Benjamin Netanyahu said.
Iranian President Masoud Pezeshkian hailed a "great victory".
Iran's authorities moved swiftly to demonstrate their control after a war that had revealed that Israel had deep intelligence about the location of Iran's leaders, and apparently had agents operating across the country.
Iran executed three men on Wednesday convicted of collaborating with Israel's Mossad spy agency and smuggling equipment used in an assassination, the Iranian judiciary's Mizan news agency reported.
Iran had arrested 700 people accused of ties with Israel during the 12-day conflict, the state-affiliated Nournews reported on Wednesday.
During the war, both Netanyahu and Trump publicly suggested it could end with the toppling of Iran's entire system of clerical rule if its leaders did not yield.
But after the ceasefire, Trump said he did not want to see "regime change" in Iran, which he said would bring chaos at a time when he wanted the situation to settle down.
