President Donald 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.
Iran's Al-Alam television said Supreme Leader Ayatollah Ali Khamenei - yet to be heard from by Saturday evening - was due to give a speech soon.
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 responded by launching missiles at Israel and at several Gulf Arab allies of the United States that host American bases.
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.
Israel's military said its pilots had hit hundreds of targets throughout Iran, including strategic defence systems already damaged in strikes last year.
It said three sites where leaders had been meeting were struck simultaneously, and several senior figures were killed.
Iran's Defence Minister Amir Nasirzadeh and Revolutionary Guards commander Mohammed Pakpour were killed in the Israeli attacks, sources said.
The first wave of strikes in what the Pentagon named "OPERATION EPIC FURY" mainly targeted Iranian officials, a source familiar with the matter said.
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."
He added: "When we are finished, take over your government. It will be yours to take. This will be probably your only chance for generations."
Oil markets have been closely watching the stand-off between Washington and Tehran to try and determine if supplies will be impacted.
Jorge Leon, head of geopolitical analysis at Rystad Energy, predicted prices could shoot up by $US10-$US20 ($A14-$A28) per barrel when markets open on Monday unless there were signs of de-escalation.
Iran, the third-largest producer in the Organisation of Petroleum Exporting Countries, pumps about four per cent of global oil supplies, and a far larger share is shipped past its coast through the strait leading out of the Gulf.
Iran's Revolutionary Guards said all US bases and interests in the region were within Iran's reach and that Iran's retaliation would continue until "the enemy is decisively defeated".
