"Khamenei, one of the most evil people in History, is dead," he posted on Truth Social.
"This is not only Justice for the people of Iran, but for all Great Americans, and those people from many Countries throughout the World, that have been killed or mutilated by Khamenei and his gang of bloodthirsty THUGS," he wrote.
"This is the single greatest chance for the Iranian people to take back their Country."
Israel's Defense Forces posted on X that "fighter jets precisely struck military targets across Iran, eliminating 7 senior officials of the Iranian Defense Leadership".
Channel 12 broadcaster reported that Trump and Israeli Prime Minister Benjamin Netanyahu had seen images of Khamenei's body after it was recovered from the rubble of his residence.
The ynet news portal also reported that the Ayatollah had been killed, citing a high-ranking Israeli official.
Earlier, Netanyahu said in a video message that there were many signs that Khamenei was no longer alive.
On Saturday morning, Israel and the United States attacked Iran, in what Israel called the largest air force operation in its history.
Around 200 fighter jets attacked about 500 targets, the Israeli military said.
Netanyahu suggested that Khamenei was dead and called on Iranians to "take to the streets and finish the job".
He said Khamenei's compound had been destroyed, and Revolutionary Guard commanders and senior nuclear officials had been destroyed.
Earlier, Iran's Al-Alam television had said Khamenei would speak, but no such speech was aired by late on Saturday.
Trump, who in the biggest foreign-policy gamble of his presidency launched the war against a foe Washington has jousted with for generations, said the strikes were aimed at ending a security threat and ensuring Iran could not develop a nuclear weapon.
He called on Iranian security forces to lay down their weapons and invited Iranians to topple their government once the bombing ended.
Tehran called the strikes, which began in the morning hours and hit targets in different areas of the country, unprovoked and illegal.
In cities across Iran, explosions caused widespread panic.
Residents rushed to collect children from school and flee areas that might be targeted.
"We are scared, we are terrified. My children are shaking, we have nowhere to go, we will die here," mother-of-two Minou, 32, said.
Iran issued a warning to shipping that the Strait of Hormuz, the narrow passage through which around a fifth of global oil consumption passes, had been closed.
Traders expected a sharp jump in oil prices.
Airlines cancelled flights in the Middle East.
Tehran promised a stronger response to come, with a senior Iranian Revolutionary Guards commander, Ebrahim Jabbari, saying it had so far used only "scrap missiles" and would soon unveil unforeseen weapons.
The UN Security Council was due to meet in New York on Saturday.
Secretary-General Antonio Guterres called for an immediate cessation of hostilities.
A girls' primary school in the southern Iranian town of Minab was hit, killing 85 people, according to the local prosecutor cited by state media. Reuters could not independently confirm the reports.
In a video message published on social media, Trump cited Washington's decades-old dispute with Iran and Iranian attacks, dating to the seizure of the US embassy in Tehran during the 1979 Islamic revolution that brought the clerics to power.
Trump said the aim was "eliminating imminent threats from the Iranian regime".
He urged Iranians to stay sheltered because "bombs will be dropping everywhere."
"When we are finished, take over your government. It will be yours to take. This will be probably your only chance for generations."
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