The IDF said two volleys of missiles were launched from Iran towards Israel in the early hours of Tuesday.
Witnesses later heard explosions near Tel Aviv and Beersheba in central Israel, where Israeli media reported a building had been struck.
Iran's foreign minister said there would be no cessation of hostilities unless Israel stopped its attacks.
Abbas Araqchi said if Israel stopped its "illegal aggression" against the Iranian people no later than 10.30 AEST, Iran had no intention of continuing its response afterwards.
"The final decision on the cessation of our military operations will be made later," Araqchi added in a post on X.
There have been no reported Israeli attacks on Iran since that time.
Trump suggested 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.
"It has been fully agreed by and between Israel and Iran that there will be a Complete and Total CEASEFIRE... for 12 hours, at which point the War will be considered, ENDED!," he said in a post on Truth Social.
"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'," Trump wrote on his Truth Social site.
Iran denies ever having a nuclear weapons program but Supreme Leader Ali Khamenei has said that if it wanted to, world leaders "wouldn't be able to stop us".
Israel, which is not a party to the international Non-Proliferation Treaty, is the only country in the Middle East believed to have nuclear weapons. Israel does not deny or confirm that.
A White House official said US Vice President JD Vance, Secretary of State Marco Rubio and US special envoy Steve Witkoff were in direct and indirect contact with the Iranians.
Neither Iran's UN mission nor the Israeli embassy in Washington 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 and had passed the message on to the United States.
Prime Minister Benjamin Netanyahu told government ministers whose discussions ended early on Tuesday not to speak publicly, Israel's Channel 12 television reported.
Earlier 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.
The president's announcement comes after Iran's military carried out a "devastating and powerful" missile attack on the Al-Udeid US air base in Qatar.
Qatar's defence minister, quoted by al-Jazeera TV, said its air defences intercepted missiles directed at the Al-Udeid air base, the largest US military installation in the Middle East, situated across the Gulf from Iran.
Iran's military said its volley against Al-Udeid air base matched the number of bombs dropped by the United States on Iranian nuclear sites over the weekend.
Iran also said it targeted the base because it was outside of populated areas.
Iran's handling of the attack recalled earlier clashes with the US and Israel, with Tehran seeking a balance between saving face with a military response but without provoking a cycle of escalation it can't afford.
Tehran appears to have achieved that goal.
Agencies
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