The euro clawed back some of the heavy losses it suffered on Monday, when it hit a 10-year low versus the yen, but it remained under pressure as traders stayed risk-averse because of a lack of indicators to push it upwards.
Tokyo rose 0.95 per cent, or 80.88 points, to 8,616.55 and Sydney was 0.85 per cent, or 34.2 points, higher at 4,072.7.
Shanghai, which was closed Monday, ended 1.06 per cent, or 26.45 points, lower at 2,471.30 as it played catch-up with the previous session's huge regional losses, while dealers are jittery about the state of China's economy.
Taipei, which was also closed Monday for a holiday, tumbled 2.88 per cent, or 219.20 points, to end at 7,391.37.
Hong Kong and Seoul were closed for the mid-autumn public holidays.
Investors are likely to buy back shares following Monday's sell-off in the absence of additional headlines showing further deterioration of the Greek debt crisis, said Kenichi Hirano, operating officer at Tachibana Securities.
But Greece-related concerns remain, Hirano told Dow Jones Newswires. "Nothing has fundamentally changed," he said.
Dealers took some solace from a report in the Financial Times that Beijing could buy bonds from Italy, which is considered one of the eurozone economies that is in danger of needing a bailout -- following Greece, Portugal and Ireland.
The news that China was "in discussions to purchase Italian debt has calmed the market; remember that China eased European tensions in the past by purchasing Spain?s debt back in January", noted Emma Lawson at National Australia Bank.
The euro fetched $1.3621 early in Europe, from $1.3680 in New York late Monday but well up from the levels near $1.3500 the previous session.
The common European currency was at 104.80 yen against 105.56 in New York after falling below 104.00 on Monday to a 10-year low.
The dollar Tuesday edged down to 76.98 yen from 77.15.
The Dow saw a late rally to end up 0.63 per cent on the China-Italy report, while the S&P 500 climbed 0.70 per cent and the Nasdaq Composite rallied 1.10 per cent.
The US gains came despite a big sell-off in Asia and Europe on Monday caused by renewed fears that Greece -- which was recently given the green light for a second bailout -- could default on its debt repayments.
Germany's Economy Minister Philipp Roesler said Monday that Europe could no longer rule out an "orderly default" for Greece, while Der Spiegel said Berlin officials were considering a possible scenario of Athens returning to the drachma if it defaults. However, the officials denied this.
New York's main oil contract, light sweet crude for delivery in October, was up 81 cents to $89 per barrel in afternoon trade.
Brent North Sea crude for October delivery gained 61 cents to $112.86.
Gold was trading at $1,818.60 an ounce at 0800 GMT on Tuesday, down from $1,841.20 in late trade Monday.
In other markets:
-- Singapore fell 0.52 per cent, 14.21 points, to close at 2,729.37.
Singapore Telecom (SingTel) was flat at Sg$3.04 and DBS Bank eased 1.22 per cent to Sg$12.20.
-- Manila closed flat, edging up 3.14 points to 4,292.91.
Philex Mining slumped 4.2 per cent to 25.95 pesos but subsidiary Philex Petroleum surged 15.8 per cent to 9.96 pesos. SM Investments was up 0.4 per cent at 552 pesos.
-- Wellington added 0.66 per cent, or 21.60 points, to 3,285.41.
Fletcher Building rose 0.8 per cent to NZ$7.71, Sky City was 1.5 per cent higher at NZ$3.45 and Telecom gained 2.0 per cent to NZ$2.52.
-- Jakarta fell 0.55 per cent, or 21.33 points, to 3,874.78.
Car distributor Astra International fell 0.6 per cent to 69,000 rupiah, nickel miner Inco slid 1.3 per cent to 3,750 rupiah and Telkom lost 0.7 per cent to 7,350 rupiah.
-- Kuala Lumpur was 0.12 per cent, or 1.74 points, higher at 1,448.00.
Telecoms company Axiata Group moved up 0.6 per cent to 4.81 ringgit and plantation firm Sime Darby gained 0.2 per cent to 8.70. Gaming giant Genting Malaysia lost 0.3 per cent to 3.39 ringgit.
-- Bangkok closed down 0.88 per cent, or 9.16 points, at 1,031.67.
-- Indian shares edged down 0.21 per cent, or 34.3 points, to 16,467.44 -- a third straight day of losses.
India's largest commercial bank, State Bank of India, fell 1.56 per cent, or 29.1 rupees, to 1,840.5.
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