Investors ran for the hills on news of the attacks and a warning from Tehran that its regional foe faced a "bitter and painful" fate, while US President Donald Trump said a "massive conflict" in the region was possible.
While Tel Aviv said it had struck military and nuclear targets, Iran said residential buildings had been hit.
Israeli Prime Minister Benjamin Netanyahu said in a video statement: "This operation will continue for as many days as it takes to remove this threat.
"We struck at the heart of Iran's nuclear enrichment programme. We targeted Iran's main enrichment facility at Natanz. We also struck at the heart of Iran's ballistic missile programme," he added.
Nuclear scientists "working on the Iranian bomb" had also been hit, he said.
In Tehran, supreme leader Ayatollah Ali Khamenei warned Israel would suffer severe consequences, issuing a statement that said: "With this crime, the Zionist regime has set itself for a bitter and painful fate and it will definitely receive it."
Israeli Defence Minister Israel Katz had earlier cautioned that "a missile and drone attack against the State of Israel and its civilian population is expected in the immediate future".
Trump previously warned that an Israeli attack could be on the cards, telling reporters at the White House: "I don't want to say imminent, but it looks like it's something that could very well happen."
The US leader said he believed a "pretty good" deal on Iran's nuclear programme was "fairly close", but that an Israeli strike on the country could wreck the chances of an agreement.
A US official said there had been no US involvement in the operation.
Still, there are worries the United States could be sucked into the crisis after Iran threatened this week to target US military bases in the region if a regional conflict broke out.
Both main oil contracts, which had rallied earlier in the week on rising tensions, spiked more than 12 percent -- hitting levels not seen since January -- amid fears about supplies of the commodity.
The rush from risk assets to safe havens saw equity markets across Asia tumble and bonds rally with gold, which popped above $3,400 an ounce. US and European equity futures were deep in the red.
"The Middle East powder keg just blew the lid off global markets," said Stephen Innes at SPI Asset Management.
"Equity futures are plummeting. Bond yields are sinking. Gold and oil are skyrocketing," he added.
"Brent crude futures are racing toward the mid-$70s range -- but if the Strait of Hormuz, which accounts for 20 percent of global oil flows, finds itself in the blast radius, you can add another $15 to the bid.
"If Iran holds back, we get a relief bounce. But if missiles start raining down on Tel Aviv or Tehran retaliates with real teeth, we're staring down a scenario that could redefine the macro narrative for the rest of 2025."
Banking giant JPMorgan Chase had warned just this week that prices could top $130 if the worst-case scenario developed.
Market sentiment had already been low after Trump sounded his trade war klaxon again by saying he would be sending letters within the next two weeks to other countries' governments to announce unilateral levies on their exports to the United States.
The "take it or leave it" deal spurred fears he would reimpose the eye-watering tolls announced on April 2 that tanked markets before he announced a 90-day pause.
- Key figures at around 0315 GMT -
West Texas Intermediate: UP 12.6 percent at $76.61 per barrel
Brent North Sea Crude: UP 12.2 percent at $77.77 per barrel
Tokyo - Nikkei 225: DOWN 1.3 percent at 37,665.93
Hong Kong - Hang Seng Index: DOWN 0.8 percent at 23,848.26
Shanghai - Composite: DOWN 0.8 percent at 3,376.40
Dollar/yen: DOWN at 143.40 yen from 143.56 yen on Thursday
Euro/dollar: DOWN at $1.1532 from $1.1583
Pound/dollar: DOWN at $1.3549 from $1.3605
Euro/pound: UP at 85.12 pence from 85.11 pence
New York - Dow: UP 0.2 percent at 42,967.62 (close)
London - FTSE 100: UP 0.2 percent at 8,884.92 (close)
dan/pst
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