The euro rebounded from morning losses to climb against the yen and US dollar as European leaders sought to sooth investor concerns, saying they were willing to work with Nicosia to help it avoid bankruptcy.
Sydney fell 0.40 percent, or 20.1 points, to 4,967.3 while Seoul lost 0.97 percent, or 19.15 points, to 1,959.41.
Bargain hunters moved in to send Hong Kong up 0.97 percent, or 214.58 points, to 22,256.44, while Shanghai surged 2.66 percent, or 59.94 points, to 2,317.37.
Tokyo was closed for a public holiday.
On Tuesday MPs rejected a proposal to impose a levy on savings as part of a deal agreed with international creditors for a 10 billion euro (US$13 billion) rescue.
The plan had been to charge 6.75 percent for deposits of 20,000-100,000 euros and a 9.9 percent tax on anything above that. Savings of up to 20,000 euros would have been exempt.
Asian markets slumped on Tuesday after an initial deal was struck at the weekend that included a tax on all savers.
The 5.8 billion euros the proposal would have raised was crucial to Nicosia getting the full rescue. With that now in doubt Cyprus must now find other ways to raise cash to repay its debts.
However, while Tuesday's events raised fears the country could exit the eurozone, analysts said they soothed fears that such levies could be introduced in other troubled eurozone countries, which could have hammered confidence in the region.
Stephen Wood, chief market strategist at Russell Investments, told Dow Jones Newswires: "We're watching very closely, but at present we don't think Cyprus is a game-changer in Europe.
"We're looking at financial-system indicators in Italy, Spain, Portugal, Greece and also bank data to see if there's a run or even a jog on banks in those countries. We don't see that just yet."
Dutch Finance Minister Jeroen Dijsselbloem said in a statement: "I confirm that the Eurogroup (of finance ministers) stands ready to assist Cyprus in its reform efforts" given Monday when it offered easier bank levy terms to reduce the impact on smaller savers.
The European Central Bank also said it would continue to provide financial support for troubled Cypriot banks, a key step to allow all sides a little more time to try to find a way out of the impasse.
But Stan Shamu, market strategist at IG Markets in Melbourne, offered a word of warning, saying: "The Cyprus issue is far from over.
"I don't think it will be a situation where the ECB has stepped in and we don't have to worry about it."
Cypriot Finance Minister Michalis Sarris was due to contact Russian officials later in the day as the government seeks other ways of finding the money such as a bond issue or bank restructuring.
On currency markets the euro climbed hopes that the crisis can be overcome.
In afternoon trade the single currency bought US$1.2898, down from US$1.2881 in New York late Tuesday, while it sat at 122.93 yen from 122.59 yen.
The dollar fetched 95.29 yen from 95.23 yen.
On Wall Street markets were mixed, with the Dow nudging up 0.03 percent, the S&P 500 falling 0.24 percent and the Nasdaq off 0.26 percent.
US traders took heart from expectations the Federal Reserve could on Wednesday deliver an improved view of the world's biggest economy.
Data Tuesday showed new housing starts rose 28 percent in February, underscoring strength in the crucial US real estate sector.
The Fed's policy committee "may sound more upbeat this time around amid the more broad-based recovery", said David Song of DailyFX in the United States.
In other markets:
-- Taipei fell 0.52 percent, or 40.44 points, to 7,798.03. Taiwan Semiconductor Manufacturing Co. fell 1.2 percent to Tw$98.8 while smartphone maker HTC was 1.0 percent lower at Tw$246.5.
-- Manila closed 0.10 percent lower, shedding 6.63 points to 6,419.62. Metropolitan Bank eased 1.40 percent to 113 pesos and Alliance Global fell 3.73 percent to 19.88 pesos, while SM Investments added 1.19 percent.
-- Wellington closed 0.10 percent higher, adding 4.39 points to 4,349.43. Air New Zealand was up 2.75 percent at NZ$1.50, Sky Television rose 1.48 percent to N$5.49 and Telecom was down 1.1 percent at NZ$2.26.
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