Iran's Islamic Revolutionary Guard Corps has vowed to avenge the death of the Supreme Leader Ayatollah Ali Khamenei.
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"The killers of the Imam of the nation will not escape severe, decisive, and deterrent punishment," the elite force said in a statement on Sunday carried by Lebanon's Hezbollah.
"The most-intense offensive operation in the history of the armed forces of the Islamic Republic of Iran will begin in moments, targeting (Israel) and American terrorist bases," it said.
The statement added that the IRGC, Iran's armed forces and Basij militias would confront "internal and external conspiracies" and punish the aggressors "with a deterrent and exemplary response".
US President Donald Trump had announced his death hours earlier, after a joint US and Israeli aerial bombardment that targeted Iranian military and governmental sites.
"Khamenei, one of the most evil people in History, is dead," Trump wrote on Truth Social.
The "heavy and pinpoint bombing" would continue through the week or as long as necessary, saying it gave Iranians their "greatest chance" to "take back" their country, he said.
Under Khamenei's leadership, the IRGC developed into the country's leading military force and became far more influential than the regular army.
Iran's state television and the state-run IRNA news agency confirmed the 86-year-old's death, on Sunday.
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, adding that "there was not a thing he, or the other leaders that have been killed along with him, could do".
There are reports Khamenei's daughter and son-in-law, daughter-in-law and a grandchild were also killed in the attacks.
Iran's government declared 40 days of public mourning and a seven-day nationwide public holiday to commemorate Khamenei's death.
Iran state TV says Khamenei was at his Tehran compound when attack began.
The state-run IRNA news agency also confirmed the death of the head of Iran's Revolutionary Guard, Major General Mohammad Pakpour, and a top security adviser Khamenei, Ali Shamkhani.
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.
The UN Security Council met 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 now faces 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.
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, although 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.
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.
with dpa