Tokyo's Nikkei ended the session up 0.19 per cent, or 20.17 points, at 10,525.19, Sydney rose 0.21 per cent, or 10.30 points, to 4,808.20 and Hong Kong climbed 1.71 per cent, or 398.51 points, to 23,711.70.
Shanghai made a late recovery to end up 0.12 per cent, or 3.73 points, at 2,999.94 after officials sought Monday to allay fears of an imminent interest rate hike.
Crude prices slipped after the United States refused to rule out tapping its oil reserves to ease the impact of high oil prices.
The Financial Times also reported that OPEC members Kuwait, the United Arab Emirates and Nigeria were joining Saudi Arabia in raising output to calm markets.
Kuwaiti oil minister Sheikh Ahmad Abdullah al-Sabah told journalists that members of the Organisation of the Petroleum Exporting countries were holding consultations over the oil market, but denied Kuwait had increased production.
"We are in consultation but have not yet decided which direction," we are heading, he said when asked if OPEC was discussing whether to raise production.
New York's main contract, light sweet crude for April delivery, fell 70 cents to $104.74 per barrel in Asian trade, while Brent North Sea crude for April dropped 64 cents to $114.40.
"Risk aversion is likely to be the dominant theme until there is reasonable certainty that oil prices can retreat to $90 or below," Ric Spooner, chief market analyst at CMC Markets in Sydney, told Dow Jones Newswires.
"The threat of a permanent rise in oil prices has hit at a time when equity markets were priced on the assumption of solid earnings growth over the next 12 to 18 months.
"Oil at over $100 per barrel for any length of time is likely to lead to reduced expectations for consumer discretionary spending and corporate profitability."
Markets got a weak lead from the United States, where the volatility in Libya and the Middle East spooked Wall Street.
The Dow Jones Industrial Average dropped 0.66 per cent, the S&P 500 index fell 0.83 per cent and the tech-rich Nasdaq Composite lost 1.40 per cent.
Gold prices also dropped back after hitting a record high of $1,440.32 in London on Monday.
Gold closed at $1,428.00-$1,429.00 an ounce in Hong Kong, down from Monday's close of $1,437.00-$1,438.00.
On currency markets, the euro was supported by anticipation of a likely interest rate rise by the European Central Bank, despite renewed worries about European sovereign debt after Moody's downgraded Greece and yields on Portugal's 10-year bonds hit a euro-era high of 7.5 per cent.
The euro firmed to $1.3982 from $1.3971 in New York on Monday. The single European currency rose to 115.00 yen from 114.82 yen.
The dollar moved narrowly against the yen, fetching 82.26 yen in Tokyo afternoon trade, little changed from 82.25 yen in New York late Monday.
In other markets:
-- Seoul rose 0.81 per cent, or 16.05 points, to 1,996.32.
-- Taipei rose 0.39 per cent, or 33.96 points, to 8,747.75.
Leading smartphone maker HTC was 1.38 per cent higher at Tw$1,100, while Taiwan Semiconductor Manufacturing Co rose 0.85 per cent to Tw$71.5.
-- Manila rose 0.32 per cent, or 12.39 points, to 3,898.87 thanks to strong corporate results.
Aboitiz Equity Ventures rose 0.71 per cent to 42.75 pesos. DMCI Holdings surged 4.79 per cent to 37.20 pesos. Semirara Mining jumped 5.10 per cent to 214.20 pesos.
-- Wellington fell 0.30 per cent, or 10.28 points, to 3,419.78.
Telecom fell 2.3 per cent to NZ$2.10 after a setback in its efforts to lead the country's broadband Internet roll-out.
Mainfreight rose 2.7 per cent to NZ$8.82 after it announced it would buy Netherlands-based Wim Bosman Group. Fletcher Building was unchanged at NZ$8.84.
-- Jakarta rose 0.52 per cent, or 18.6 points, to 3,580.31.
-- Singapore rose 1.22 per cent, or 37.32 points, to 3,103.84.
Oversea-Chinese Banking Corp rose 2.05 per cent to Sg$9.48 and Singapore Airlines climbed 1.63 per cent to Sg$13.72.
-- Kuala Lumpur edged up 0.13 per cent, or 1.92 points, to 1,517.66.
Malaysia Airlines rose 1.70 per cent to 1.84 ringgit, gaming group Genting was up 1.20 per cent at 10.38, while telecoms company Axiata dropped 1.20 per cent to 4.90.
-- Bangkok rose 1.56 per cent, or 15.63 points, to 1,018.57.
Coal miner Banpu rose 1.1 per cent to 736.00 and energy firm PTT Plc climbed 1.7 per cent to 348.00.
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