A senior Israeli official told Reuters the Iranian leader's body had been found after a strike on Saturday and President Donald Trump said the US worked closely with Israel to target the man who led Iran since 1989.
Iranian news agencies Tasnim and Mehr, however, reported that the supreme leader was "steadfast and firm in commanding the field".
Iran called the strikes unprovoked and illegal and responded with missiles fired at Israel and at least seven other countries, including Gulf states that host US bases.
Trump, who made the biggest foreign-policy gamble of his presidency after campaigning for re-election as a "peace president", said the strikes were aimed at ending a decades-long threat from Iran and ensuring it could not develop a nuclear weapon.
Intelligence and tracking systems kept track of Khamenei's whereabouts, Trump wrote in a Truth Social post, adding that "there was not a thing he, or the other leaders that have been killed along with him, could do".
Trump reiterated calls for Iranians to topple the government but warned: "The heavy and pinpoint bombing, however, will continue, uninterrupted throughout the week or, as long as necessary to achieve our objective of PEACE THROUGHOUT THE MIDDLE EAST AND, INDEED, THE WORLD!"
Israeli Prime Minister Benjamin Netanyahu said Khamenei's compound had been destroyed.
Iran's Defence Minister Amir Nasirzadeh and Revolutionary Guards commander Mohammed Pakpour were killed in the Israeli attacks and Israel's military said five other senior military commanders were among the dead.
In cities across Iran, explosions caused widespread panic.
After confronting hundreds of Iranian missile and drone attacks in response, the Pentagon said there were no US deaths or injuries.
Iran warned 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 previously unseen weapons.
The UN Security Council was due to meet in New York on Saturday, with Secretary-General Antonio Guterres calling for an immediate cessation of hostilities.
Israel's military said some 200 fighter jets had completed the largest flying mission in its history, hitting 500 targets throughout Iran, including strategic defence systems already damaged in strikes last year.
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.
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," he wrote.
But he faced pushback from opposition Democrats, and a few of his fellow Republicans, who said a prolonged campaign against Iran would be illegal without congressional approval and that lawmakers should vote within days.
Iran's clerical leaders were already in a difficult position after mass anti-government demonstrations in January, which led to a crackdown in which thousands of people were killed in the worst domestic unrest since the era of the 1979 revolution.
Israeli military operations over the past two years had already killed some of Iran's senior military officials and severely weakened several of Tehran's once-feared proxy forces across the Middle East.
After Israel pounded Iran in a 12-day air war in June, joined by the US, Israel had warned they would strike again if Iran pressed ahead with its nuclear and ballistic missile programs.
Jorge Leon, head of geopolitical analysis at Rystad Energy, predicted oil prices could shoot up by $US10 ($A14) to $US20 ($A28) per barrel when markets open on Monday, if there is no sign of de-escalation.
In Israel, sirens and mobile-phone warnings sent Israelis rushing to air raid shelters as Iran launched a series of missile barrages that were mostly intercepted, though some missiles hit.
Emergency teams in Tel Aviv treated at least 20 people hurt by a missile that hit a residential building, Israel's ambulance service said. Photos from the scene showed one side of the multi-storey building blown out and its roof caved in.
Loud booms sounded in Abu Dhabi, capital of the United Arab Emirates, an oil producer and close US ally, and several blasts were heard in the business capital Dubai, where one of the city's plush hotel districts was also hit.
Bahrain said the service centre of the US Fifth Fleet - base for American naval forces in the region - had been subjected to a missile attack.
Qatar said it had downed all missiles targeting the country and that it had a right to respond. Kuwait confirmed a missile attack on a US military base there.
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