While the international community anxiously watches events in Eastern Europe, analysts said the fact that the crisis had not worsened had provided a buying opportunity.
The dollar and euro also clawed back some of Monday's losses against the yen as a certain degree of confidence returned to the market, while oil prices fell back after hitting multi-month highs.
Tokyo rose 0.47%, or 69.25 points, to 14,721.48, Sydney added 0.29%, or 15.9 points, to close at 5,400.2 and Hong Kong ended 0.70% higher, adding 156.96 points to 22,657.63
Shanghai shed 0.18%, or 3.76 points, to 2,071.47 after rallying almost 1% on Monday. And Seoul gave up 0.54%, or 10.58 points, to 1,954.11.
"The immediate and likely largest impact from the risk-off sentiment due to the crisis in the Ukraine may have already passed," Norihiro Fujito, senior investment strategist at Mitsubishi UFJ Morgan Stanley Securities, told Dow Jones Newswires.
World shares tumbled on Monday after Russia's parliament voted to allow President Vladimir Putin to send troops into Crimea, a mainly Russian-speaking peninsula in the southeast of the ex-Soviet state.
It came in response to last month's ousting of the pro-Russian government in Kiev of Viktor Yanukovych, after weeks of protests in the capital.
Russia's move was met with world condemnation and warnings of possible political and economic isolation, with Washington and the European Union saying they were looking at a range of sanctions.
As Ukraine accused Russia of giving its forces in Crimea an ultimatum to surrender, US President Barack Obama said Moscow was on the "wrong side of history" in the region's biggest crisis since the Cold War.
The United States has also suspended military cooperation with Russia.
In Moscow the MICEX closed down 10.79% and the other main Russian market, the RTS, closed down 12.01%, while the ruble sank to record lows against the dollar and euro.
However, David Baran, co-CEO of Symphony Financial Partners, a Tokyo-based hedge fund, said: "The Russian-Ukraine standoff may drag on, but a military confrontation with the West is likely well out of the question.
"The economic stakes of the crisis are not that great for the rest of the world, either."
In foreign exchange trading the dollar rose to 101.82 yen compared with 101.44 yen in New York Monday.
The euro bought $1.3755 and 140.10 yen against $1.3737 and 139.34 yen.
The yen had surged on Monday as investors scurried into safer investments in response to the events in Europe.
Oil prices fell after jumping on Monday on fears that Russia, a key supplier to Europe, could switch off its pipeline to the West.
US benchmark West Texas Intermediate for April delivery eased $1.24 cents to $103.68, having touched its highest level since early October.
Brent North Sea crude for April fell $1.60 to $109.60 after rallying to its strongest levels since the end of December.
Gold fetched $1,337.62 an ounce at 0810 GMT compared with $1,347.10 late Monday.
In other markets, Taipei fell 0.55%, or 47.44 points, to 8,554.54.
Taiwan Semiconductor Manufacturing Co was 0.46% lower at T$107.5, while leading chip design house MediaTek dropped 1.11% to T$445.
Wellington added 0.52%, or 25.86 points, to 5,033.26. Trade Me was up 1.02% at NZ$3.95 and Fletcher Building gained 1.06% to close at NZ$9.55.
Manila eased 0.20%, or 12.92 points, to close at 6,394.60.
Ayala Corp slipped 1.23% to 562 pesos and Philippine Long Distance Telephone Co added 0.52% to 2,720 pesos.