Oil prices have steadied as Middle East events kept investors nervous, while caution ahead of an expected US interest rate cut kept wider financial markets in tight ranges.
European stocks were subdued, with luxury stocks one of the few sectors seeing activity.
MSCI's broadest index of Asia-Pacific shares outside Japan ticked up 0.08 per cent while Japan's Nikkei dipped 0.18 per cent after 10 straight days of gains and China's blue-chip share index rose 0.49 per cent.
Wall Street futures pointed to a softer opening.
Brent crude futures dipped 0.26 per cent to $US64.38 a barrel, having conceded about 65 per cent of their gains made after the weekend attack on Saudi Arabia's oil facilities.
Brent crude futures dipped 0.09 per cent to $US64.48 a barrel, having conceded a chunk of their gains made after the weekend attack on Saudi Arabia's oil facilities.
US West Texas Intermediate (WTI) crude lost 0.5 per cent to $US59.04 per barrel, paring back around half of its gains after Saturday's attack.
Saudi Energy Minister Prince Abdulaziz bin Salman on Tuesday sought to reassure markets, saying the kingdom would restore its lost oil production by month-end having recovered supplies to customers to the levels they were prior to the weekend's attacks.
"I would think a spike in oil prices will likely prove to be short-term given that the global economy isn't doing too well," said Akira Takei, bond fund manager at Asset Management One.
Still, heightened geopolitical tensions underpinned oil as well as some safe-haven assets such as US bonds.
A US official said on Tuesday the United States believes the attacks originated in southwestern Iran, an assessment that could heighten the rivalry between Tehran and Riyadh. Iran has denied involvement in the strikes.
Adding to uncertainties in the Middle East were exit polls from Israel's election, which showed the race too close to call suggesting Prime Minister Benjamin Netanyahu's fight for political survival could drag on.
Gold was 0.07 per cent down at $US1,501.54, while the 10-year US Treasuries yield fell to 1.799 per cent, compared with Friday's 1-1/2-month high of 1.908 per cent ahead of the Fed's policy announcement on Wednesday.
While a 25-basis point rate cut is seen as near-certain, investors look to the statement and economic projections from Fed policymakers, given signs of deep disagreements among them.
"People are very cautious right now," said Christophe Barraud, at Market Securities in Paris.
"They're waiting for the Fed meeting and potential new development in Saudi Arabia."
"For the Fed meeting, people are not betting on a big positive surprise."
The ongoing US-China trade war has raised policymakers' concerns about slowing factory output although resilient domestic consumption has given hawks some reasons to worry about cutting rates too hastily.
Possibly further complicating their discussions, short-term US interest rates shot up this week, with overnight repo rates rising to 7.0 per cent, due largely to seasonal factors such as huge payments for taxes and bond supply.
That prompted the New York Fed to conduct its first repo operation in more than a decade to inject funds to stressed money markets.
Also in focus is the Bank of Japan's policy meeting due Thursday.
While the latest Reuters poll suggests the BOJ will keep its policy on hold, 28 of 41 economists expect it will ease its policy this year and 13 believe it may surprise by taking action at the Thursday meeting.
In currencies, sterling edged lower after climbing to a new six-week high on hopes for a last-minute Brexit deal.
Against the euro sterling was unchanged at 88.585 pence .
The yen eased slightly to 108.21 yen, near a 1-1/2-month low of 108.37 touched on Tuesday.
Australian Associated Press