Iranian media reported strikes nationwide on Saturday, and smoke could be seen rising from the capital.
President Donald Trump said in a video posted on social media that the US had begun "major combat operations in Iran".
He claimed Iran has continued to develop its nuclear program and plans to develop missiles to reach US and appealed to the Iranian people to "take over your government — it will be yours to take".
Trump acknowledged that there could be American casualties following Iran strikes, saying "that often happens in war".
It wasn't immediately clear whether the 86-year-old Khamenei was in his offices at the time of the strike. He hasn't been seen publicly in days as tensions with the United States have grown.
However, a source told Reuters Khamenei was not in Tehran and had been transferred to a secure location.
The attack comes as the United States has assembled a vast fleet of fighter jets and warships in the region to try to pressure Iran into a deal over its nuclear program.
Iran has said it hasn't enriched since June, but it has blocked international inspectors from visiting the sites America bombed during a 12-day war then. Satellite photos analysed by The Associated Press have shown new activity at two of those sites, suggesting Iran is trying to assess and potentially recover material there.
Iran currently has a self-imposed limit on its ballistic missile program, limiting their range to 2000 kilometres. That puts all the Mideast and some of eastern Europe in their range.
There is no public evidence of Iran seeking to have intercontinental ballistic missiles, though Washington has criticised its space program as potentially allowing it to one day.
Iran has vowed to respond if attacked, including saying American military personnel and bases spread across the region would be targets.
Hours after the strikes on Iran, explosions rocked northern Israel as the country worked to intercept incoming Iranian missiles.
The blasts echoed just after the Israeli military said it would be using its air defence systems to bring down the Iranian fire. There was no immediate word on any damage or casualties from the ongoing attack.
Several hospitals in Israel launched their emergency protocols, including moving patients and surgeries to underground facilities.
Roads to Khamenei's compound in downtown Tehran had been shut down by authorities as other blasts rang out across the capital. Neighbouring Iraq closed its airspace, according to the Ministry of Transport.
Targets in the Israeli campaign included Iran's military, symbols of government and intelligence targets, according to an official briefed on the operation, who spoke on condition of anonymity to discuss non-public information on the attack.
Israeli Defence Minister Israel Katz described the attack as being done "to remove threats." He did not immediately elaborate.
Trump wanted a deal to constrain Iran's nuclear program, and he sees an opportunity while the country is struggling at home with growing dissent following nationwide protests.
Iran had hoped to avert a war, but maintains it has the right to enrich uranium and does not want to discuss other issues, like its long-range missile program or support for armed groups like Hamas and Hezbollah.
In Tehran, witnesses heard the first blast by Khamenei's office. Iranian state television later reported on the explosion, without offering a cause.
More explosions struck Iran's capital after Israel said it was attacking the country. Authorities have offered no casualty information from the strikes.
Meanwhile, Iran shut down its airspace and mobile phone services were cut.
The warning to pilots came out as explosions rang out across Tehran.
- with Reuters
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