Trump says both sides are violating the truce and warns Israel: "Don't drop those bombs."

US President Donald Trump on Tuesday accused both Israel and Iran of violating the ceasefire hours after announcing it, expressing particular frustration with Tel Aviv, which had announced major new attacks on Tehran.

"Israel. Don't drop those bombs. Doing so is a major violation. Bring your pilots home, now!" Trump wrote on Truth Social shortly after leaving the White House to travel to a NATO summit in The Hague.

Before boarding the plane, the US president told reporters that he was "not happy" with either side for violating the truce, particularly Israel.

"I have to get Israel to calm down now," Trump said as he left the White House. "Israel, as soon as we made the deal, came out and dropped a bomb load, the likes of which I've never seen before, the biggest bomb load we've ever seen," he added.

Iran and Israel have been fighting "so long and so hard that they don't know what the hell they're doing," he said before turning away from the cameras and heading for his helicopter.

Earlier, Israeli Defense Minister Israel Katz said he had ordered the military to launch new attacks on targets in Tehran in response to what he said were Iranian missiles launched in a "flagrant violation" of the ceasefire.

Iran denied launching missiles and claimed that the Israeli attacks had lasted an hour and a half beyond the scheduled start time of the ceasefire.

Despite the initial violations, there was a palpable sense of relief in both countries, in the wider Middle East, and around the world that a path out of the war had been established, 12 days after Israel launched it with a surprise attack and two days after Trump joined the war with attacks on Iranian nuclear targets.

"We are happy, very happy. Who mediated or how it happened doesn't matter. The war is over. It should never have started in the first place," Reza Sharifi, 38, told Reuters by telephone. He was returning to Tehran from Rasht on the Caspian Sea, where he had moved with his family to escape attacks on the capital.

Arik Daimant, a computer engineer in Tel Aviv, said: "Unfortunately, it's a little late for me and my family, because our house here was completely destroyed in the recent bombings last Sunday . But as they say, 'better late than never,' and I hope this ceasefire will be a new beginning."

Trump had announced the ceasefire with a post on Truth Social: "THE CEASEFIRE IS NOW IN EFFECT . PLEASE DO NOT VIOLATE IT."