Israel has bombed a target near Tehran despite an expletive-laden rebuke from US President Donald Trump for launching air strikes hours after agreeing to a ceasefire deal with Iran.

Trump scolded both Iran and Israel, saying both had been fighting so long neither knew “what the f— they are doing” after early violations of the truce he announced on Monday (US time).

Trump directed particularly stinging criticism at Israel over the scale of its strikes, telling it to “calm down now”.

He said Israel called off further attacks at his command to preserve the deal to end a 12-day air war with Iran, after the biggest military confrontation between the Middle East arch-foes raised fears of global repercussions.

Following those remarks, however, two witnesses reached by telephone in the Iranian capital said they heard two loud blasts.

Israeli 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 3½ hours after the ceasefire was meant to begin.

It said Israel had decided to refrain from further attacks following a call between Netanyahu and Trump. It did not explicitly say if the strike on the radar site came before or after the phone call.

Iran denied launching any missiles and said Israel’s attacks had continued for 90 minutes beyond when the truce was meant to start.

Iranian President Masoud Pezeshkian said later that Iran would not violate the ceasefire unless Israel did, and that it was prepared to return to the negotiating table, according to state-run Nournews.

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Trump, en route to a NATO summit in Europe, had admonished Israel with an obscenity in an extraordinary early morning 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.

Before departing the White House, Trump said 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.

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Iran and Israel had been fighting “so long and so hard that they don’t know what the f— they’re doing”.

A reporter for Axios said Netanyahu had told Trump that Israel would scale back the bombing mission rather than cancel it.

“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!”

Despite the initial reports of violations, there was a palpable sense of relief in both countries 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 air strikes.

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.”

On board Air Force One heading to the NATO summit, Trump said he did not want Iran’s rulers to be 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.

The ceasefire came the morning after Iran responded to the US participation in the air strikes with a volley of missiles at the biggest American military base in the Middle East, located in Qatar.

No one was hurt in that strike as the Iranian retaliation appeared to have been calibrated carefully to allow de-escalation.

‘Not our war’: Australian Iranians

The ceasefire will not calm the fears of Iranians in Australia as their homeland’s authoritarian regime looms over their loved ones.

The Australian-Iranian community’s feelings are more complicated.

They live in fear of US or Israeli bombs killing their friends and family while also worrying about the threat Iran’s autocratic Islamic government poses for their loved ones.

No one person or voice could speak for an entire group, Australian Iranian Community Alliance vice-president Suren Edgar said. However, he believed most Iranians were unhappy with the current regime.

“This is not our war, we didn’t create this war but we are paying the price,” he said.

“If the outcome of the ceasefire would be to keep the Islamic Republic in power, that won’t be safe for the international community and won’t be safe for the people inside Iran.”

For some, like Persian Australian Community Association member Nader Ranjbar, there was hope the conflict could help de-stabilise the Iranian autocracy and pave the way for a new, democratic government.

He remained concerned the current administration would intensify its persecution of Iranian people.

Iranian Australians are concerned about the safety of their relatives after the end to hostilities. Photo: AAP

“That’s my worst fear,” he said.

“That somehow they get away from this mess and the first thing they do is start killing Iranian people.

“We are all worried about our family and friends and the whole country.”

There was also confusion as to whether a ceasefire would last.

Deputy Prime Minister Richard Marles said Australia was concerned about the risks of escalation.

“We don’t want to see the ceasefire broken – that’s the fundamental point here,” he told ABC’s 7.30.

“Clearly, what is in the interests of the region and the world, and both countries here, is that the ceasefire is maintained and we have a de-escalation.”