WASHINGTON/DOHA/ISTANBUL - US President Donald Trump said that a "complete and total" ceasefire between Israel and Iran will go into force with a view to ending the 12-day conflict between the two nations, moments after both sides threatened new attacks.

While an Iranian official confirmed that Tehran had agreed to a ceasefire, there was no immediate comment yet from Israel.

A senior White House official said Israel had agreed so long as Iran does not launch further attacks and that Trump brokered the deal in a call with Israeli Prime Minister Benjamin Netanyahu.

Trump appeared to suggest that Israel and Iran would have some time to complete any missions that are underway, at which point the ceasefire would begin in a staged process.

"On the assumption that everything works as it should, which it will, I would like to congratulate both Countries, Israel and Iran, on having the Stamina, Courage, and Intelligence to end, what should be called, 'THE 12 DAY WAR'," he wrote on his Truth Social site.

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.

Trump told Qatar's emir that Israel had agreed to the ceasefire, according to the official.

Neither Iran's UN mission nor the Israeli embassy in Washington immediately responded to separate requests for comment from Reuters.

Hours earlier, three Israeli officials had signalled Israel was looking to wrap up its campaign in Iran soon and had passed the message on to the United States.

Netanyahu had told government ministers whose discussions ended early on Tuesday not to speak publicly, Israel's Channel 12 television reported.

S&P 500 futures rose 0.4 per cent late on Monday, suggesting traders expect the US stock market to open with gains on Tuesday.

US crude futures fell in early Asian trading hours on Tuesday to their lowest level in more than a week after Trump said a ceasefire had been agreed, relieving worries of supply disruption in the region.

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End to the fighting?

There did not appear to be calm yet in the region.

The Israeli military issued two evacuation warnings in less than two hours to residents of areas in the Iranian capital Tehran, one late on Monday and one early on Tuesday.

Israeli Army radio reported early on Tuesday that alarms were activated in the southern Golan Heights area due to fears of hostile aircraft intrusion.

Earlier on Monday, Trump said he would encourage Israel to proceed towards peace after dismissing Iran's attack on an American air base that caused no injuries and thanking Tehran for the early notice of the strikes.

Iran's attack came after US bombers dropped 30,000-pound (14,000kg) bunker-busters on Iranian underground nuclear facilities at the weekend, joining Israel's air war against Iran in a conflict that has entered its 12th day.

Much of Tehran's population of 10 million has fled after days of bombing.

The Trump administration maintains that its aim was solely to destroy Iran's nuclear programme, not to open a wider war.

But in a social media post on Sunday, Trump spoke of toppling the hardline clerical rulers who have been Washington's principal foes in the Middle East since Iran's 1979 Islamic Revolution.

Israel, however, had made clear that its strikes on Evin prison - a notorious jail for housing political prisoners - and other targets in Tehran were intended to hit the Iranian ruling apparatus broadly, and its ability to sustain power.

Source: Reuters