Nikkei futures in Chicago pointed to a fall of about 0.4 percent in Tokyo shares following a 1.3 percent fall on Monday, while MSCI's broadest index of Asia-Pacific shares outside Japan sagged 0.1 percent.
As investors flocked to safe assets for fear of further escalation in geopolitical tensions, gold stood near a four-month high while the yield on U.S. Treasuries yield dropped to a one-month low, reflecting higher prices for the bonds.
Russia's Black Sea fleet denied reports it had given Ukrainian forces in Crimea an ultimatum to surrender by early on Tuesday or face attack, Interfax news agency said. But Ukraine's acting president said Russia's military presence in Crimea was growing.
The United States, which seeks to isolate Moscow through sanctions, said any such threat would be a dangerous escalation.
The European Union also threatened unspecified "targeted measures" unless Russia returns its forces to their bases and opens talks with Ukraine's new government.
Fear of a military confrontation pummelled Russian financial markets, with the rouble-denominated MICEX stock index diving 10.8 percent.
The rouble fell two percent against the dollar to a record low of 36.50 to the dollar even as the Russian central bank raised interest rates to stem capital flight and to defend the currency.
"The latest situation could look like a new Cold War. Lack of clear, strong leadership in the world could lead to a more fragmented world, destabilising the global economy. More funds will flow to safe assets for the time being,"said Daisuke Uno, chief strategist at Sumitomo Mitsui Bank.
On Wall Street, the S&P 500 index lost 0.7 percent, to 1,845.73 as concerns over Ukraine overwhelmed generally upbeat economic data on the U.S. economy.
Financial data firm Markit's gauge of U.S. factory activity rose in February to its highest level since May 2010.
Separately, the Institute for Supply Management said its index of U.S. factory activity rose to 53.2 in February, topping expectations. Personal spending in January grew despite the harsh winter weather.
The data helped to underpin the dollar, with the dollar index rebounding from a two-month low hit on Friday to stand at 80.059, compared to Friday's low of 79.688. The euro stood at $1.3710, off Friday's peak of $1.38255.
Investors' risk averse mood helped the yen, which stood near one-month high against the U.S. dollar. The yen fetched 101.44 yen to the dollar, not far from a one-month high of 101.20 hit on Monday.
Gold, another major safe haven, traded at $1,350 per ounce, just below Monday's four-month high of $1,354.80.
Gains in U.S. Treasuries sent the benchmark 10-year yield to a one-month low of 2.592 percent as prices rose.
Fear of possible armed conflict boosted oil prices. U.S. crude futures, which have been rising for weeks due to cold winter in many parts of the United States, stood near a five-month high hit on Monday. They were last at $104.65 per barrel, near Monday's high of $105.22.