Iran's UN mission declined to comment on Trump's ceasefire announcement, and the Israeli mission said it had no immediate comment.
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.
"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.
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.
Trump told Qatar's emir that Israel had agreed to the ceasefire, according to the official.
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.
On Sunday, Prime Minister Benjamin Netanyahu said Israel was "very, very close to completing" its goals.
A senior Iranian official told Reuters that Tehran had agreed to the US-proposed ceasefire.
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.
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.
Trump had earlier thanked Iran for giving the US notice prior to shooting missiles at the military base, which he said made it possible for no lives to be lost.
Iranian authorities threatened to retaliate against the United States after US bombers dropped bunker-busters on Iranian nuclear sites in Fordow, Natanz and Esfahan at the weekend in support of Israel.
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.
The attack came shortly after Qatar closed its airspace as a precaution and the US and UK urged its citizens in the country to "shelter in place".
Just before the explosions, Iranian President Masoud Pezeshkian wrote on the social platform X: "We neither initiated the war nor seeking it. But we will not leave invasion to the great Iran without answer".
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.
US military official says no US bases in Iraq were targeted but that a malfunctioning Iranian missile aimed at Israel triggered an alert in Iraq earlier in the day.
with AP and PA
