The MSCI's broadest index of Asia-Pacific shares outside Japan was up 0.1%, helped by a 0.3% rise in Australian shares and as the Standard & Poor's 500 Index neared its all-time high the previous session.
South Korean shares opened 0.2% higher.
The key monthly US nonfarm payrolls report on Friday will likely confirm market views that the Federal Reserve will wish to maintain its extremely accommodative monetary policy, which underpinned investor sentiment and sharpened risk appetites.
Analysts expect 2,00,000 jobs were added to payrolls last month and the unemployment rate to hold steady at 7.7%, far above the Fed's desired 6.5% goal that would prompt a change in its current policy stance.
Ahead of the payrolls, data on private-sector hiring by payrolls processor ADP is due later this session, followed by Thursday's latest weekly jobless claims.
Tuesday's data showed new orders for US factory goods rose sharply in February but a gauge of planned business spending slipped, suggesting factory activity continued to expand at a moderate pace. Earlier this week, the Institute for Supply Management's index of national factory activity fell in March.
"We get a sense that the US economy is not running ahead of itself but is growing ... a rather familiar but nonetheless solidly asset-friendly set of figures," Kit Juckes, strategist at Societe Generale, said in a note to clients.
"The 'gentle recovery and mad money' combination which has been driving markets is intact, risk is quietly 'on' in credit and stocks ... and it all contrasts dramatically with Euro-shambles."
The euro held steady around $1.2819, struggling to move far away from a four-month low of $1.2750 touched last week, as the currency remained pressured by concerns about bailout consequences in Cyprus and weak euro zone economies.
Markit's Eurozone Manufacturing PMI fell in March to 46.8 from 47.9 in February, the 20th straight month that the index has come in below the 50 mark that separates growth and contraction, boosting expectations that European Central Bank President Mario Draghi could offer a dovish tone at the ECB's policy meeting on Thursday.
Cyprus on Tuesday concluded a 10 billion euro rescue deal with international lenders in which big depositors took massive losses.
The Bank of Japan will start its two-day policy meeting later in the day, the first under the new governor Haruhiko Kuroda. Market expectations have been running high for Kuroda to announce at his inaugural policy meeting an increase in bond purchases and a lengthening in the maturities of bonds the BOJ intends to buy.
The Nikkei stock average opened up 0.9% after tumbling to a one-month low on Tuesday.
The dollar was down 0.1% against the yen at 93.31, but off a one-month low of 92.57 yen touched on Tuesday. The euro was down 0.1% against the yen at 119.63, hovering near its lowest since February 26 of 119.15 yen seen on Tuesday.
US crude futures fell 0.4% to $96.78 a barrel.
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