Iran warned U.S. President Donald Trump against being dragged into all-out war in the Middle East after the attacks, which Washington and Riyadh blame on Tehran.
About half of Saudi crude production was disabled, putting severe limits on the country's spare capacity, a cushion for global oil markets if an outage occurs.
"The Saudi oil industry could be threatened again, and we could see more supply disruption from the Persian Gulf," said Gene McGillian, vice president of market research at Tradition Energy in Stamford, Connecticut.
Brent crude futures, the global benchmark, gained 80 cents to settle at $64.40 a barrel, while U.S. West Texas Intermediate crude settled up 2 cents at $58.13 a barrel.
European banking shares <.SX7P> rose 1.9% and the Swiss franc posted its biggest gain in two weeks after the Swiss National Bank declined to match the European Central Bank and the Fed in easing monetary policy.
Major central banks have been loosening policy, mostly by cutting rates, to stem a slowdown in global growth.
Upbeat U.S. data suggests the U.S. economy is still on a moderate growth path. The number of Americans filing for unemployment benefits increased less than expected last week, pointing to strong labor market conditions.
The pan-regional FTSEurofirst 300 <.FTEU3> index of leading European shares closed up 0.64%. MSCI's gauge of stocks across the globe <.MIWD00000PUS> rose 0.08%, paring gains that put the index within 1% of its record high.
MSCI's emerging markets index <.MSCIEF> fell 0.6%.
Gains in Microsoft Corp pushed the S&P 500, the U.S. equity benchmark, closer to its record high, while a rally in bank stocks lifted European shares after the Fed set a higher bar for further rate reductions on Wednesday.
Microsoft, the biggest U.S. stock by market cap, valued at $1.08 trillion, hit $142.37 before paring some gains to close up 1.8% at $141.07. The S&P 500 at one point traded 6 points below its all-time peak of 3,027.98 set in July.
Wall Street closed little changed, with the Dow Jones Industrial Average falling 52.29 points, or 0.19%, to 27,094.79. The S&P 500 gained 0.06 points, or 0.00%, to 3,006.79 and the Nasdaq Composite added 5.49 points, or 0.07%, to 8,182.88.
The U.S. dollar fell against the euro, the Swiss franc and the Japanese yen after the Fed cut rates by 25 basis points on Wednesday to provide insurance against the risk of weaker global growth and resurgent U.S-China trade tensions.
Sterling jumped, rising 0.64% to $1.2548, after European Commission President Jean-Claude Juncker said a Brexit deal is possible.
The dollar index <.DXY> fell 0.21%, with the euro up 0.12% to $1.1042. The Japanese yen strengthened 0.39% versus the greenback at 108.05 per dollar.
U.S. Treasury yields fell after division appeared among policymakers on whether the Fed would cut rates further and as pressures in the short-term funding markets eased.
Benchmark 10-year notes <US10YT=RR> fell 3/32 in price to push their yield down to 1.7944%.
U.S. gold futures settled down about $9, or 0.6%, to $1,506.20 an ounce.
(Reporting by Herbert Lash; Editing by Lisa Shumaker and Dan Grebler)
By Herbert Lash