MSCI's broadest index of Asia-Pacific shares outside Japan was down 0.1%. Japanese stocks slid 0.48%, while Australian shares were down 0.18%.
"There is certainly a risk-off tone, but I'm surprised the markets are not reacting more," said Tsutomu Soma, general manager of fixed income business solutions at SBI Securities in Tokyo.
"The U.S. and other countries have oil reserves, which helps sentiment in a case like this. You also have a lot of positions riding on the Fed meeting."
Brent crude, the international benchmark, fell 1.2% to $68.18 per barrel in Asia on Tuesday. On Monday Brent surged by 14.6% for its biggest one-day percentage gain since at least 1988.
U.S. West Texas Intermediate futures were down 1.7% to $61.86 per barrel in Asia following a 14.7% surge on Monday, the biggest one-day gain since December 2008.
The drone attack over the weekend has cut the kingdom's oil production in half, creating the biggest disruption to global oil supplies in absolute terms since the overthrow of the Iranian Shah in 1979, International Energy Agency data show.
U.S. President Donald Trump has authorised the release of emergency crude stockpiles if needed, which could ease some upward pressure on crude futures, but risks to the outlook abound.
Trump said on Monday it looked like Iran was behind the attacks but stressed that he did not want to go to war, which was a slightly less bellicose tone than his initial reaction.
Iran has rejected U.S. charges that it was behind the attacks. Tension between the two countries were already running high over Iran's ambitions for nuclear weapons. The strikes in Saudi Arabia are likely to raise regional tensions even further.
In Asia on Tuesday, U.S. stock futures rose 0.05%, but sentiment remained fragile. On Wall Street, the S&P 500 ended 0.31% lower.
Spot gold traded a shade higher in Asia at $1,498.60 an ounce following a 0.7% increase on Monday.
The yield on benchmark 10-year Treasury notes fell slightly to 1.8327%
The dollar was little changed at 108.17 yen. Some traders said it would be difficult to take big positions in the currency pair before the outcome of two important central bank meetings this week.
The Federal Reserve is expected to cut interest rates at a policy meeting ending on Wednesday, which could put pressure on the Bank of Japan to ease policy at a meeting the following day.
Traders are also focused on the U.S.-Sino trade war.
Deputy-level talks between the United States and China are scheduled to start in Washington on Thursday, paving the way for high-level talks next month aimed at resolving a bitter trade row that has dragged on for more than a year.
Any sign of progress to put an end to the trade war between the world's two-largest economies could help improve risk sentiment, but negotiations have been fraught, making it difficult to judge whether the two sides can narrow their differences.
(Editing by Sam Holmes) ((firstname.lastname@example.org; +81 3 6441 1984 twitter.com/stanleywhite1;))