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Tokyo ended the session up 1.22 per cent, or 129.94 points, at 10,754.03 as exporter stocks got a boost from a weaker yen -- a result of dealers moving out of the safe-haven Japanese currency amid renewed risk appetite. Hong Kong edged up 0.06 per cent.
Shanghai was barely changed from Monday after a top official suggested inflation would fall in February, boosting investor hopes that further interest rate hikes in the near term can be avoided. Taipei rose 1.49 per cent, or 127.91 points, to end at 8,727.56.
Sydney ended lower however after the Australian central bank said it would keep rates on hold at 4.75 per cent and forecast inflation within its 2-3 per cent target this year, but added that monetary policy would remain mildly restrictive.
The S&P/ASX 200 index fell 0.11 per cent, or 5.3 points, to 4,826.40.
Seoul was closed for a public holiday.
Traders welcomed Saudi Arabia's commitment on Monday to increase oil production in case of a supply shortfall caused by the unrest across the oil-rich Middle East and North Africa, particularly Libya.
Saudi Arabia, the largest producer in the OPEC oil cartel, said its cabinet had met and discussed the anti-regime protests shaking Libya "and their repercussion on oil production in that country".
Saudi Arabia "is committed to the stability of the market" and to ensuring that oil supplies remain available, it said in a statement.
New York's benchmark West Texas Intermediate contract for April delivery rose 44 cents to $97.41 and Brent North Sea crude for April was up 62 cents at $112.42.
While oil prices were up, they remained well short of last week's peaks, when Brent soared close to $120.
The news came as the United States hit Libyan leader Moamer Kadhafi with a record $30 billion in sanctions and said it was ready to assist pro-democracy protesters who have overrun key cities in the oil-rich North African state.
Protests that have sprung up across the region from Tunisia and Algeria to Egypt and Oman have now spread to Djibouti and Kuwait, increasing concerns for the region.
Tokyo's Nikkei index was lifted by a weaker yen as concerns over the Middle East eased and dealers shifted attention to hopes for recovery in the US economy.
"It will be easier to shift from pessimistic to optimistic sentiment this week on the back of a recovery in the US economy," Masayoshi Yano, senior market analyst at Meiwa Securities, told Dow Jones Newswires.
The dollar was trading at 82.14 yen in early Tokyo trade, up from 81.79 in New York late Monday. The euro rose to 113.40 yen from 112.90 and was sitting at $1.3819 from $1.3803.
In China, hopes that rates will not be hiked in the near term were lifted after Zhang Ping, the director of the nation's top economic planning agency, was quoted as saying inflation in February was likely to turn out lower than January's 4.9 per cent.
Two manufacturing indexes also suggested a slowdown in activity.
The HSBC Manufacturing PMI, or purchasing managers index, fell to a seven-month low of 51.7 in February from 54.5 in January, while a government survey showed factory production fell to a six-month low of 52.2 in February from 52.9 in January.
A reading above 50 indicates expansion while below 50 means contraction.
The easing follows a series of measures by Beijing to rein in the economy and inflation, including three rate hikes in four months and increases in the amount of money banks must keep in reserve.
However, the data was tempered by figures showing input prices rose for the third month in a row, fuelling inflation.
Regional markets were given a strong cue by the Dow, which gained 0.79 per cent on Monday thanks to merger and acquisition activity.
Gold opened at $1,410.00-$1,411.00 an ounce, down from Monday's close of $1,411.30-$1,412.30.
In other markets:
-- Manila rose 0.46 per cent, or 17.50 points, to 3,784.23.
Aboitiz Power added 1.91 per cent to 29.35 pesos and Metropolitan bank gained 3.31 per cent to 59.30 pesos, but Philippine Long Distance Telephone fell 0.92 per cent to 2,140 pesos.
-- Wellington closed 0.41 per cent, or 13.87 points, higher at 3,384.39.
Telecom ended up 3.4 per cent at NZ$2.15 and Sky City rose 1.5 per cent to NZ$3.30, but Fletcher Building ended down 0.3 per cent at NZ$8.74.
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