The surge in oil prices boosted share prices of energy companies, while global stock markets won support also from the prospect of US interest rate cuts this year.
Rising hopes of a rate cut helped to offset lingering tensions over the long-running trade war between Washington and Beijing.
Thursday's reported tanker attacks, the second incident involving shipping in the strategic sea lane in a matter of weeks, sent London's Brent North Sea oil rebounding more than four percent in morning deals before trimming gains.
The Gulf of Oman lies at the other end of the strategic Strait of Hormuz from the Gulf, part of a vital shipping lane through which at least 15 million barrels of crude oil and hundreds of millions of dollars of non-oil imports pass.
According to Iranian state media, one of the tankers -- the Norwegian-owned Front Altair -- was carrying ethanol from Qatar to Taiwan, while the Kokuka Courageous was carrying methanol from Saudi Arabia to Singapore.
- 'Tension is high' -
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"Tension across the Middle East is high -- and the attacks on two tankers has further exacerbated the situation, even though there does not appear to have been any damage to the cargos," said John Hall, chairman of British-based consultancy Alfa Energy.
"As a consequence the market has responded dramatically with an increase in the oil price of (as much as) four percent," he told AFP.
"How long it will hold for is another matter -- and it has already fallen back slightly."
In afternoon London trading, Brent for August delivery pulled back to stand at $61.99 per barrel, up $2.02, or nearly 3.4 percent from Wednesday.
New York's West Texas Intermediate was up $1.60 or around 3.1 percent at $52.74 per barrel.
It was a huge turnaround for the oil market, which had slumped Wednesday on news of soaring crude inventories in the United States that indicated weak demand growth.
Thursday's reported attacks came amid simmering tensions between Tehran and Washington, which pointed the finger at key oil producer Iran over previous tanker attacks in May.
Markets are paying particularly close attention after US President Donald Trump abandoned a landmark 2015 nuclear deal with the Islamic republic last year.
- Retaliation fears -
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"Investors will be keeping a keen eye on the developments in the Gulf of Oman as tensions in the Middle-East have been rising since President Trump withdrew from the Iran deal," Sun Global Investments chief Mihir Kapadia said in a note.
"Although US National Security Adviser John Bolton has accused Iran of a similar incident before, the country has distanced itself from today's attacks.
"From this, the biggest concern will be a retaliation which could leave markets looking shaky in the meantime, with Iran potentially being met with more severe sanctions which could really affect its oil output and economy if found guilty," Kapadia added.
Meanwhile, Geordie Wilkes, head of research at Sucden Financial, said: "It is too soon to compare recent action to the 1980s when there was a tanker war between Iran and Iraq as they attempted to stop each other from exporting oil."
However, he warned that "persistent attacks could increase risks high enough for vessels to not travel through the area," a development that would force energy prices higher.
In commodity deals elsewhere, cocoa prices retreated one day after striking an 11-month peak.
The market had soared Wednesday on news that key producers Ivory Coast and Ghana have threatened to stop selling their production to buyers who do not meet a minimum price level.
- Key figures around 1330 GMT -
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Oil - Brent North Sea: UP $2.02 at $61.99 per barrel
Oil - West Texas Intermediate: UP $1.60 at $52.74 per barrel
London - FTSE 100: UP 0.06 percent at 7,372.34 points
Frankfurt - DAX 30: UP 0.6 percent at 12,182.22
Paris - CAC 40: UP 0.1 percent at 5,381.93
EURO STOXX 50: UP 0.2 percent at 3,394.61
New York - Dow: UP 0.3 percent at 26,091.47
Tokyo - Nikkei 225: DOWN 0.5 percent at 21,032.00 (close)
Hong Kong - Hang Seng: DOWN 0.1 percent at 27,294.71 (close)
Shanghai - Composite: UP 0.1 percent at 2,910.74 (close)
Euro/dollar: DOWN at $1.1276 from $1.1287 at 2100 GMT
Pound/dollar: DOWN at $1.2691 from $1.2737
Dollar/yen: DOWN at 108.47 yen from 108.50 yen