Russian stocks and the ruble gained while gold and the safe-haven Japanese yen fell sharply after President Vladimir Putin ordered back troops that took part in military exercises in central and western Russia.
There was no word, however, on Russian forces that have effectively occupied much of Crimea, and financial assets failed to retrace the entirety of the sharp moves seen globally on Monday.
European stock markets opened higher, with the pan-European FTSEurofirst 300 .FTEU3 up 1.1 percent, recouping some of the previous session's steep losses.
"There's a perception that maybe we're going to see a ratcheting down of tensions and there's a possibility that President Putin may be open to dialogue... that's why markets are bouncing," Michael Hewson, chief market analyst at CMC Markets UK, said.
"I would be sitting on the sidelines still because it's a very fluid situation. We're going to continue to see a certain amount of volatility and it would be a brave investor who dives back in now."
The FTSEurofirst 300 had sunk 2.2 percent on Monday, with Russian also having paid a heavy financial price for its military intervention in Ukraine's Crimea region.
Russian stocks, bonds and the ruble had plunged as Putin's forces tightened their grip in Crimea, whose population is mainly ethnic Russian. The ruble-denominated MICEX stock index was up 3.3 percent on Tuesday.
MSCI's broadest index of Asia-Pacific shares outside Japan .MIAPJ0000PUS added about 0.2 percent in afternoon trade.
The Nikkei .N225 ended up 0.5 percent, erasing earlier losses, on cautious bargain-hunting by investors hopeful that conflict will be avoided.
The euro stood at $1.3757, up about 0.2 percent. While it remained off Friday's peak of $1.38255, it hit its session high of $1.3773 after news of the Russian troop move to base.
Investors were looking for clues from European producer price data, out at 1000 GMT, after European Central Bank President Mario Draghi said on Monday that inflation in the euro zone is "way below" the European Central Bank's goal.
He added the longer it stays at such low levels the harder it will be to get it back up to the target, and low inflation has stoked talk that the bank could take policy action to ward off the threat of deflation, perhaps as early as a policy meeting on Thursday.
Yields on top-rated European bonds rose as investors moved out of safe-haven assets, while yields on the lower-rated Italian and Spanish bonds remained close to eight-year lows, showing remarkable resilience to global risk aversion in a further sign worries over the euro zone debt crisis have eased.
"Turn the clock back a few years and these markets would be hit by contagion," said Nick Stamenkovic, a bond strategist at RIA Capital Markets in Edinburgh.
"But you see more signs of growth in these countries ...(and) the ECB has backstops in place."
Investors' risk-averse mood had helped the yen, whose gains unraveled late in the session after the Russian developments. The yen fetched 101.77 yen to the dollar, down 0.3 percent, and moved away from a one-month high of 101.20 hit on Monday.
Gold, another traditional safe-haven asset, skidded 0.8 percent late in the Asian session, trading at $1,339.84 per ounce at 0846 GMT, after the risk-averse mood saw it touch a four-month high of $1,354.80 on Monday .
Gains in U.S. Treasuries sent the benchmark 10-year yield to a one-month low of 2.592 percent as prices rose on Monday, but the yield was last at 2.633 percent in Europe, up from its U.S. close of 2.608 percent.
The Australian dollar pared initial gains after the Reserve Bank of Australia kept rates steady at a record low, as widely expected. The Aussie was flat at the end of Asian trade, although it edged higher again at the start of the European day to $0.8959.
(Additional reporting by Lisa Twaronite, Hideyuki Sano and Tomo Uetake in Tokyo, Francesco Canepa and Marius Zaharia in London)
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