Adding downward pressure to sentiment was a decision by Fitch to downgrade 18 Spanish banks while the euro was steady against the dollar and yen.
Tokyo closed up 0.60 percent, or 51.12 points, at 8,587.84, while Hong Kong climbed 0.82 percent, or 153.96 points, to 19,026.52 and Shanghai gained 1.27 percent, or 29.13 points, to 2,318.92.
Seoul rose 0.25 percent, or 4.58 points, to close at 1,859.32, but Sydney slipped 0.22 percent, or 9.1 points, to finish at 4,063.8.
The early euphoria over eurozone finance chiefs' weekend agreement to a bailout for Spain's banks of up to $125 billion has evaporated amid concerns the government will now need a rescue as its borrowing costs have soared.
Spanish 10-year government bonds yields the rate of return earned by investors spiked to a record 6.834 percent, the highest level since the eurozone was founded, before easing slightly.
The 10-year yield on bonds in Italy, another troubled economy, leapt to a high of 6.301 percent from the previous day's closing level of 6.032 percent.
Meanwhile Fitch slashed the ratings of 18 Spanish banks, a day after it cut the country's two biggest lenders, Santander and BBVA.
Fitch, which cut Spain's sovereign debt rating by three notches last week to "BBB", said its latest move was the result of the potential for the loan portfolios of certain banks to deteriorate further.
Despite the news, markets in the US and Europe were higher, with repeated calls by the European Central Bank for a common banking union to bolster the region's financial system providing some reassurance.
Also Chicago Federal Reserve Bank President Charles Evans reiterated his support for more monetary stimulus ahead of next week's meeting of the Federal Open Market Committee.
On Wall Street the Dow rose 1.31 percent, the S&P 500 gained 1.17 percent and the Nasdaq Composite advanced 1.19 percent.
In Europe stock markets in London, Frankfurt, Paris and Madrid all posted gains and extended them in the first few minutes of trade on Wednesday.
"Many investors remain on the fence, awaiting the outcome of Greece's upcoming elections, so risk capital is sparse," Monex market analyst Toshiyuki Kanayama told Dow Jones Newswires.
Traders fear that Sunday's general election in Greece, the second in six weeks, could end in a victory for anti-austerity groups who would tear up a bailout agreement in a move that would lead to Athens exiting the eurozone.
The euro bought $1.2512 in Tokyo afternoon trade, down from $1.2502 in New York late Tuesday.
Against the Japanese currency, the common European unit inched up to 99.60 yen from 99.44 yen, while the dollar firmed to 79.54 yen from 79.52 yen.
On oil markets New York's main contract, light sweet crude for delivery in July, eased 24 cents to $83.08 a barrel and Brent North Sea crude for July rose 16 cents to $97.30 a barrel.
Gold was worth $1,612.90 an ounce at 0810 GMT, compared with $1,590.50 late Tuesday. In other markets: Taipei closed 0.24 percent, or 16.75 points, higher at 7,088.83. Smartphone maker HTC rose 1.45 percent to Tw$350.0 while Taiwan Semiconductor Manufacturing Co. ended up 0.76 percent at Tw$80.0.
Manila closed 0.66 percent, or 33.76 points, up at 5,109.61. SM Investments gained 0.14 percent to 701 pesos and DMCI Holdings added 0.18 percent to 56 pesos but Philippine Long Distance Telephone dropped 0.65 percent to 2,440Reuters
Wellington fell 1.28 percent, or 43.87 points, to 3,381.73. Fletcher Building was off 2.4 percent at NZ$6.13, Telecom was down 2.3 percent at NZ$2.33 and Contact Energy slipped 1.9 percent to NZ$4.62.