However, while Israel called the attack -- which Tehran said was in response to a strike on its Syrian embassy -- an escalation of hostilities, analysts said there was hope among traders that the crisis could be contained.
That sliver of optimism helped drag oil prices lower.
Saturday's bombardment of more than 300 ballistic and cruise missiles and attack drones -- which were mostly repelled by air defences -- compounded worries about the outlook for US interest rates following more forecast-beating inflation and jobs data.
Iran told the United Nations the strike was a "legitimate" defensive response to the attack in Damascus on April 1, which killed seven Revolutionary Guards including two generals.
It added on social media that "the matter can be deemed concluded" but warned that "should the Israeli regime make another mistake, Iran's response will be considerably more severe".
Israeli military spokesman Daniel Hagari said it was "a severe and dangerous escalation".
But experts said the limited scope of the attack showed Iran was seeking to make a show of strength with its attack, but without sparking a conflict.
Meanwhile, US President Joe Biden was reported to have cautioned Israeli Prime Minister Benjamin Netanyahu to "take the win" and forego a counterattack.
Still, Saxo's Redmond Wong said: "All eyes remain on whether there will be any response from Israel and markets will likely be volatile in the day ahead to any geopolitical headlines."
Asian markets mostly fell Monday, though they pared their initial big losses.
Tokyo, Hong Kong, Seoul, Sydney, Wellington, Singapore, Mumbai, Taipei and Manila were all in the red.
Shanghai rose more than one percent after China on Friday unveiled fresh market regulatory measures that one analyst said could help its long-term performance.
London was lower in the morning session, while Frankfurt and Paris rose.
US futures rose, having dropped sharply on Friday as investors went nervously into the weekend.
"The muted market response likely stems from the highly intricate sentiment in the market at this stage," said IG Markets' Hebe Chen.
"Market participants are certainly not giving up hope that the past weekend's events were just a one-off occurrence, while holding their breath for what could happen next."
With worries about an escalation subsiding for now, oil prices dipped, though observers warned they could spike back above $100 if the crisis worsens.
"This war may move down the escalation ladder if the Israeli government follows the advice of the White House and forgoes retaliatory action," said Helima Croft at RBC Capital Markets.
The broadly risk-off mood sent the dollar up to a new 34-year high against the yen, putting Japanese officials in the spotlight after they said they were ready to step in to support their currency.
- Key figures around 0810 GMT -
Tokyo - Nikkei 225: DOWN 0.7 percent at 39,232.80 (close)
Hong Kong - Hang Seng Index: DOWN 0.7 percent at 16,600.46 (close)
Shanghai - Composite: UP 1.3 percent at 3,057.38 (close)
London - FTSE 100: DOWN 0.4 percent at 7,960.09
Dollar/yen: UP at 153.88 yen from 153.24 yen on Friday
Euro/dollar: UP at $1.0661 from $1.0645
Pound/dollar: UP at $1.2472 from $1.2449
Euro/pound: DOWN at 85.45 pence from 85.48 pence
West Texas Intermediate: DOWN 1.1 percent at $84.71 per barrel
Brent North Sea Crude: DOWN 1.0 percent at $89.58 per barrel
New York - Dow: DOWN 1.2 percent at 37,983.24 (close)
-- Bloomberg News contributed to this story --
dan/mtp
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